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25 tháng 2 2019
\(\frac{x+5}{95}+\frac{x+3}{97}+\frac{x+1}{99}=\frac{x+15}{85}+\frac{x+20}{80}+\frac{x+25}{75}.\)
\(\frac{x+5}{95}+1+\frac{x+3}{97}+1+\frac{x+1}{99}+1-\frac{x+15}{85}-1-\frac{x+20}{80}-1-\frac{x+25}{75}-1=0\)
\(\frac{x+100}{95}+\frac{x+100}{97}+\frac{x+100}{99}-\frac{x+100}{85}-\frac{x+100}{80}-\frac{x+100}{75}=0\)
\(\left(x+100\right).\left(\frac{1}{95}+\frac{1}{97}+\frac{1}{99}-\frac{1}{85}-\frac{1}{80}-\frac{1}{75}\right)=0\)
\(\Rightarrow x+100=0\Rightarrow x=-100\)
\(\frac{1}{95}+\frac{1}{97}+\frac{1}{99}-\frac{1}{85}-\frac{1}{80}-\frac{1}{75}\ne0\)
4 tháng 5 2020
ĐKXĐ: \(x\ne0\)
Ta có: \(\frac{10}{x}+2\left(\frac{1}{80}-\frac{1}{x}\right)=\frac{2}{15}\)
\(\Leftrightarrow\frac{8}{x}+\frac{1}{40}-\frac{2}{15}=0\)
\(\Leftrightarrow\frac{960}{120x}+\frac{3x}{120x}-\frac{16x}{120x}=0\)
\(\Leftrightarrow960+3x-16x=0\)
\(\Leftrightarrow960-13x=0\)
\(\Leftrightarrow13x=960\)
hay \(x=\frac{960}{13}\)(tm)
Vậy: \(x=\frac{960}{13}\)
31 tháng 1 2020
Câu c : \(x^4-3x^3+2x^2-9x+9=0\)
<=>\(x^4-x^3-2x^3+2x^2-9x+9=0\)
<=>\(x^3\left(x-1\right)-2x^2\left(x-1\right)-9\left(x-1\right)=0\)
<=>\(\left(x-1\right)\left(x^3-2x^2-9\right)=0\)
<=> \(x-1=0\) hoặc \(x^3-2x^2-9=0\)
Nếu x-1=0 <=> x=1
Nếu \(x^3-2x^2-9=0\)
<=> \(x^3-3x^2+x^2-9=0\)
<=>\(x^2\left(x-3\right)+\left(x-3\right)\left(x+3\right)=0\)
<=>\(\left(x-3\right)\left(x^2+x+3\right)=0\)
Vì \(x^2+x+3=\left(x+\frac{1}{2}\right)^2+\frac{11}{4}\) >0 nên x-3=0 <=> x=3
Vậy \(S=\left\{1;3\right\}\)
31 tháng 1 2020
Câu b : \(x^2+\left(\frac{x}{x+1}\right)^2=\frac{5}{4}\)
<=> \(4x^2\left(x^2+2x+2\right)=5\left(x^2+2x+1\right)\)
<=> \(4x^4+8x^3+8x^2=5x^2+10x+5\)
<=>\(4x^4+8x^3+3x^2-10x-5=0\)
<=>\(4x^4-4x^3+12x^3-12x^2+15x^2-15x+5x-5=0\)
<=>\(\left(x-1\right)\left(4x^3+12x^2+15x+5\right)=0\)
<=>\(\left(x-1\right)\left(2x+1\right)\left(2x^2+5x+5\right)=0\)
<=>x=1 hoặc \(x=\frac{-1}{2}\)
Phương trình \(2x^2+5x+5=0\) Vô nghiệm
MN
31 tháng 1 2020
a) \(ĐKXĐ:x\ne-1;x\ne-3;x\ne-8;x\ne-10\)
\(\frac{2}{x^2+4x+3}+\frac{5}{x^2+11x+24}+\frac{2}{x^2+18x+8x}=\frac{9}{52}\)
\(\Leftrightarrow\frac{2}{\left(x+1\right)\left(x+3\right)}+\frac{5}{\left(x+3\right)\left(x+8\right)}+\frac{2}{\left(x+10\right)\left(x+8\right)}-\frac{9}{52}=0\)
\(\Leftrightarrow\frac{104\left(x+10\right)\left(x+8\right)+260\left(x+1\right)\left(x+10\right)+104\left(x+1\right)\left(x+3\right)-9\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
Đoạn này cậu tự phân tích tử rồi rút gọn nhé :D Vì hơi dài nên viết ra đây sẽ rối, k đẹp mắt cho lắm :>
\(\Leftrightarrow\frac{-927x^2+1782x+9072-9x^4-198x^3}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x^4+22x^3+103x^2-198x-1008\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x^4-3x^3+25x^3-75x^{^2}+178x^2-534x+336x-1008\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left[x^3\left(x-3\right)+25x^2\left(x-3\right)+178x\left(x-3\right)+336\left(x-3\right)\right]}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x-3\right)\left(x^3+25x^2+178x+336\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x-3\right)\left(x^3+14x^2+11x^2+154x+24x+336\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x-3\right)\left[x^2\left(x+14\right)+11x\left(x+14\right)+24\left(x+14\right)\right]}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x-3\right)\left(x+14\right)\left(x^2+11x+24\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)=0}\)
\(\Leftrightarrow\frac{-9\left(x+14\right)\left(x-3\right)\left(x+3\right)\left(x+8\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x+14\right)\left(x-3\right)}{52\left(x+1\right)\left(x+10\right)}=0\)
\(\Leftrightarrow-9x^2-99x+378=0\)
\(\Leftrightarrow x^2+11x-42=0\)
\(\Leftrightarrow\left(x+14\right)\left(x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+14=0\\x-3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-14\\x=3\end{cases}}}\)
Vậy tập nghiệm của phương trình là : \(S=\left\{-14;3\right\}\)
b) \(ĐKXĐ:x\ne-1\)
\(x^2+\left(\frac{x}{x+1}\right)^2=\frac{5}{4}\)
\(\Leftrightarrow x^2+\frac{x^2}{\left(x+1\right)^2}-\frac{5}{4}=0\)
\(\Leftrightarrow\frac{4x^2\left(x^2+2x+1\right)+4x^2-5\left(x^2+2x+1\right)}{\left(x+1\right)^2}=0\)
\(\Leftrightarrow4x^4+8x^3+4x^2+4x^2-5x^2-10x-5=0\)
\(\Leftrightarrow4x^2+8x^3+3x^2-10x-5=0\)
\(\Leftrightarrow4x^4+2x^3+6x^3+3x^2-10x-5=0\)
\(\Leftrightarrow2x^3\left(2x+1\right)+3x^2\left(2x+1\right)-5\left(2x+1\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(2x^3+3x^2-5\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(2x^3-2x^2+5x^2-5x+5x-5\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left[2x^2\left(x-1\right)+5x\left(x-1\right)+5\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(2x+1\right)\left(x-1\right)\left(2x^2+5x+5\right)=0\)
\(\Leftrightarrow2x+1=0\)
hoặc \(x-1=0\)
hoặc \(2x^2+5x+5=0\)
\(\Leftrightarrow\) \(x=-\frac{1}{2}\left(tm\right)\)
hoặc \(x=1\left(tm\right)\)
hoặc \(\left(x+\frac{5}{4}\right)^2+\frac{55}{16}=0\left(ktm\right)\)
Vậy tập nghiệm của phương trình là : \(S=\left\{-\frac{1}{2};1\right\}\)
c) \(x^4-3x^3+2x^2-9x+9=0\)
\(\Leftrightarrow x^4-x^3-2x^3+2x^2-9x+9=0\)
\(\Leftrightarrow x^3\left(x-1\right)-2x^2\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-2x^2-9\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[\left(x^3-3x^2\right)+\left(x^2-9\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x-3\right)+\left(x-3\right)\left(x+3\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)\left(x^2+x+3\right)=0\)
\(\Leftrightarrow\)\(x-1=0\)
hoặc \(x-3=0\)
hoặc \(x^2+x+3=0\)
\(\Leftrightarrow\)\(x=1\left(tm\right)\)
hoặc \(x=3\left(tm\right)\)
hoặc \(\left(x-\frac{1}{2}\right)^2+\frac{11}{4}=0\left(ktm\right)\)
Vậy tập nghiệm của phương trình là :\(S=\left\{1;3\right\}\)
KN
3 tháng 2 2020
\(ĐKXĐ:x\ne-1;x\ne-3;x\ne-8;x\ne-10\)
\(pt\Leftrightarrow\frac{2}{\left(x+1\right)\left(x+3\right)}+\frac{5}{\left(x+3\right)\left(x+8\right)}+\frac{2}{\left(x+8\right)\left(x+10\right)}=\frac{9}{52}\)
\(\Leftrightarrow\frac{\left(x+3\right)-\left(x+1\right)}{\left(x+1\right)\left(x+3\right)}+\frac{\left(x+8\right)-\left(x+3\right)}{\left(x+3\right)\left(x+8\right)}+\frac{\left(x+10\right)-\left(x+8\right)}{\left(x+8\right)\left(x+10\right)}\)
\(=\frac{9}{52}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+8}+\frac{1}{x+8}-\frac{1}{x+10}=\frac{9}{52}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+10}=\frac{9}{52}\)
\(\Leftrightarrow\frac{9}{\left(x+1\right)\left(x+10\right)}=\frac{9}{52}\)
\(\Leftrightarrow\left(x+1\right)\left(x+10\right)=52\)
\(\Leftrightarrow x^2+11x+10=52\)
\(\Leftrightarrow x^2+11x-42=0\)
\(\Delta=11^2+4.42=289,\sqrt{289}=17\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{-11+17}{2}=3\\x=\frac{-11-17}{2}=-14\end{cases}}\)
Vậy pt có 2 nghiệm là 3 và -14
NV
16 tháng 7 2016
ĐKXĐ: \(x\ne\left\{0;-1;-2;-3;-4;-5;-6;-7\right\}\)
\(\frac{1}{x}+\frac{1}{x+2}+\frac{1}{x+5}+\frac{1}{x+7}=\frac{1}{x+1}+\frac{1}{x+3}+\frac{1}{x+4}+\frac{1}{x+6}\)
\(\Rightarrow\frac{1}{x}+\frac{1}{x+7}+\frac{1}{x+2}+\frac{1}{x+5}=\frac{1}{x+1}+\frac{1}{x+6}+\frac{1}{x+3}+\frac{1}{x+4}\)
\(\Rightarrow\frac{x+7+x}{x\left(x+7\right)}+\frac{x+5+x+2}{\left(x+2\right)\left(x+5\right)}=\frac{x+6+x+1}{\left(x+1\right)\left(x+6\right)}+\frac{x+4+x+3}{\left(x+3\right)\left(x+4\right)}\)
\(\Rightarrow\frac{2x+7}{x^2+7x}+\frac{2x+7}{x^2+7x+10}=\frac{2x+7}{x^2+7x+6}+\frac{2x+7}{x^2+7x+12}\)
\(\Rightarrow\left(2x+7\right)\left(\frac{1}{x^2+7x}+\frac{1}{x^2+7x+10}-\frac{1}{x^2+7x+6}-\frac{1}{x^2+7x+12}\right)=0\)
mà \(\frac{1}{x^2+7x}+\frac{1}{x^2+7x+10}-\frac{1}{x^2+7x+6}-\frac{1}{x^2+7x+12}\ne0\)
=> 2x + 7 = 0 => x = -7/2
Vậy x = -7/2
NT
1
NV
Nguyễn Việt Lâm
Giáo viên
8 tháng 4 2019
ĐKXĐ: \(x\ne\left\{-10;-8;-3;-1\right\}\)
\(\frac{2}{\left(x+1\right)\left(x+3\right)}+\frac{5}{\left(x+3\right)\left(x+8\right)}+\frac{2}{\left(x+8\right)\left(x+10\right)}=\frac{9}{52}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+8}+\frac{1}{x+8}-\frac{1}{x+10}=\frac{9}{52}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+10}=\frac{9}{52}\)
\(\Leftrightarrow\frac{9}{\left(x+1\right)\left(x+10\right)}=\frac{9}{52}\)
\(\Leftrightarrow\left(x+1\right)\left(x+10\right)=52\)
\(\Leftrightarrow x^2+11x-42=0\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-14\end{matrix}\right.\)
21 tháng 4 2020
Bài 1:
1, \(\frac{2x-5}{x+5}=3\) (ĐKXĐ: x \(\ne\) -5)
\(\Leftrightarrow\) \(\frac{2x-5}{x+5}=\frac{3\left(x+5\right)}{x+5}\)
\(\Rightarrow\) 2x - 5 = 3(x + 5)
\(\Leftrightarrow\) 2x - 5 = 3x + 15
\(\Leftrightarrow\) 2x - 3x = 15 + 5
\(\Leftrightarrow\) -x = 20
\(\Leftrightarrow\) x = -20 (TMĐKXĐ)
Vậy S = {-20}
2, \(\frac{4}{x+1}=\frac{3}{x-2}\) (ĐKXĐ: x \(\ne\) -1; x \(\ne\) 2)
\(\Leftrightarrow\) \(\frac{4\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}=\frac{3\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}\)
\(\Rightarrow\) 4(x - 2) = 3(x + 1)
\(\Leftrightarrow\) 4x - 8 = 3x + 3
\(\Leftrightarrow\) 4x - 3x = 3 + 8
\(\Leftrightarrow\) x = 11 (TMĐKXĐ)
Vậy S = {11}
3, \(\frac{5}{2x-3}=\frac{1}{x-4}\) (ĐKXĐ: x \(\ne\) \(\frac{3}{2}\); x \(\ne\) 4)
\(\Leftrightarrow\) \(\frac{5\left(x-4\right)}{\left(2x-3\right)\left(x-4\right)}=\frac{2x-3}{\left(2x-3\right)\left(x-4\right)}\)
\(\Rightarrow\) 5(x - 4) = 2x - 3
\(\Leftrightarrow\) 5x - 20 = 2x - 3
\(\Leftrightarrow\) 5x - 2x = -3 + 20
\(\Leftrightarrow\) 3x = 17
\(\Leftrightarrow\) x = \(\frac{17}{3}\) (TMĐKXĐ)
Vậy S = {\(\frac{17}{3}\)}
Bài 2:
1, \(\frac{1}{x-1}+\frac{2}{x+1}=\frac{5x-3}{x^2-1}\) (ĐKXĐ: x \(\ne\) \(\pm\) 1)
\(\Leftrightarrow\) \(\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{2\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{5x-3}{\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow\) x + 1 + 2(x - 1) = 5x - 3
\(\Leftrightarrow\) x + 1 + 2x - 2 = 5x - 3
\(\Leftrightarrow\) 3x - 1 = 5x - 3
\(\Leftrightarrow\) 3x - 5x = -3 + 1
\(\Leftrightarrow\) -2x = -2
\(\Leftrightarrow\) x = 1 (KTM)
\(\Rightarrow\) Pt vô nghiệm
Vậy S = \(\varnothing\)
2, \(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x^2-2x}\) (ĐKXĐ: x \(\ne\) 2; x \(\ne\) 0)
\(\Leftrightarrow\) \(\frac{x\left(x+2\right)}{x\left(x-2\right)}-\frac{x-2}{x\left(x-2\right)}=\frac{2}{x\left(x-2\right)}\)
\(\Rightarrow\) x(x + 2) - x + 2 = 2
\(\Leftrightarrow\) x2 + 2x - x + 2 = 2
\(\Leftrightarrow\) x2 + x = 2 - 2
\(\Leftrightarrow\) x2 + x = 0
\(\Leftrightarrow\) x(x + 1) = 0
\(\Leftrightarrow\) x = 0 hoặc x + 1 = 0
\(\Leftrightarrow\) x = 0 và x = -1
Ta có: x = 0 KTM đkxđ
\(\Rightarrow\) x = -1
Vậy S = {-1}
3, \(\frac{5}{x-3}-\frac{3}{x+3}=\frac{3x}{x^2-9}\) (ĐKXĐ: x \(\ne\) \(\pm\) 3)
\(\Leftrightarrow\) \(\frac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{3\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{3x}{\left(x-3\right)\left(x+3\right)}\)
\(\Rightarrow\) 5(x + 3) - 3(x - 3) = 3x
\(\Leftrightarrow\) 5x + 15 - 3x + 9 = 3x
\(\Leftrightarrow\) 2x + 24 = 3x
\(\Leftrightarrow\) 2x - 3x = 24
\(\Leftrightarrow\) -x = 24
\(\Leftrightarrow\) x = -24 (TMĐKXĐ)
Vậy S = {-24}
Chúc bn học tốt!!
Mình tính mãi vẫn có chỗ sai, mong bạn thông cảm!!
22 tháng 4 2020
Mình bt mình sai đâu r Garuda
câu 3 bài 3 cuối có cái đoạn 2x + 24 = 3x
\(\Leftrightarrow\) 2x - 3x = -24 (đoạn kia mình ghi là 24 nên quên không đổi dấu)
\(\Leftrightarrow\) -x = -24
\(\Leftrightarrow\) x = 24
Vậy S = {24}
(mình sửa lại rồi nha, chắc hết chỗ sai rồi)
ĐKXĐ: ...
\(\Leftrightarrow400x-360\left(x+1\right)=x\left(x+1\right)\)
\(\Leftrightarrow x^2+x=40x-360\)
\(\Leftrightarrow x^2-39x+360=0\Rightarrow\left[{}\begin{matrix}x=24\\x=15\end{matrix}\right.\)
B giải hộ mình vs : \(\frac{80}{x-4}+\frac{80}{x+4}=\frac{25}{3}\)