Giải phương trình: 1/3(x-2)+1/4x(x-2)-1/5(x-2)=23/30
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\(a,x-5\left(x-2\right)=6x\\ \Leftrightarrow x-5x+10-6x=0\\ \Leftrightarrow-10x+10=0\\ \Leftrightarrow x=1\\ b,2^3+3x^2-32x=48\\ \Leftrightarrow3x^2-32x+8=48\\ \Leftrightarrow3x^2-32x-40=0\)
Nghiệm xấu lắm bn
\(c,\left(3x+1\right)\left(x-3\right)^2=\left(3x+1\right)\left(2x-5\right)^2\\ \Leftrightarrow c,\left(3x+1\right)\left[\left(2x-5\right)^2-\left(x-3\right)^2\right]\\ \Leftrightarrow\left(3x+1\right)\left(2x-5-x+3\right)\left(2x-5+x-3\right)=0\\ \Leftrightarrow\left(3x+1\right)\left(x-2\right)\left(3x-8\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=2\\x=\dfrac{8}{3}\end{matrix}\right.\)
\(d,9x^2-1=\left(3x+1\right)\left(4x+1\right)\\ \Leftrightarrow\left(3x+1\right)\left(4x+1\right)-\left(3x-1\right)\left(3x+1\right)=0\\ \Leftrightarrow\left(3x+1\right)\left(4x+1-3x+1\right)=0\\ \Leftrightarrow\left(3x+1\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=-2\end{matrix}\right.\)
\(b,2x^3+3x^2-32x-48=0\\ \Leftrightarrow\left(2x^3-8x^2\right)+\left(11x^2-44x\right)+\left(12x-48\right)=0\\ \Leftrightarrow2x^2\left(x-4\right)+11x\left(x-4\right)+12\left(x-4\right)=0\\ \Leftrightarrow\left(x-4\right)\left(2x^2+11x+12\right)=0\\ \Leftrightarrow\left(x-4\right)\left[\left(2x^2+8x\right)+\left(3x+12\right)\right]=0\\ \Leftrightarrow\left(x-4\right)\left[2x\left(x+4\right)+3\left(x+4\right)\right]=0\\ \Leftrightarrow\left(x-4\right)\left(2x+3\right)\left(x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{3}{2}\\x=-4\end{matrix}\right.\)
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Bài 1 :
\(\frac{4x-5}{x-1}=\frac{2+x}{x-1}\)ĐK : x \(\ne\)1
\(\Leftrightarrow\frac{4x-5}{x-1}-\frac{2-x}{x-1}=0\Leftrightarrow\frac{4x-5-2+x}{x-1}=0\)
\(\Rightarrow5x-7=0\Leftrightarrow x=\frac{7}{5}\)( tmđk )
Vậy tập nghiệm của phuwong trình là S= { 7/5 }
b, \(\frac{x-1}{x-2}-3+x=\frac{1}{x-2}\)ĐK : x \(\ne\)2
\(\Leftrightarrow\frac{x-1}{x-2}-\left(3-x\right)=\frac{1}{x-2}\)
\(\Leftrightarrow\frac{x-1}{x-2}-\frac{\left(3-x\right)\left(x-2\right)}{x-2}=\frac{1}{x-2}\)
\(\Leftrightarrow\frac{x-1-3x+6+x^2-2x-1}{x-2}=0\)
\(\Rightarrow x^2-4x+4=0\Leftrightarrow\left(x-2\right)^2=0\Leftrightarrow x=2\)( ktmđkxđ )
Vậy phương trình vô nghiệm
c, \(1+\frac{1}{2+x}=\frac{12}{x^3+8}\)ĐK : x \(\ne\)-2
\(\Leftrightarrow\frac{\left(x+2\right)\left(x^2-2x+4\right)+x^2-2x+4-12}{\left(x+2\right)\left(x^2-2x+4\right)}=0\)
\(\Rightarrow x^3+8+x^2-2x+4-12=0\)
\(\Leftrightarrow x^3+x^2-2x=0\Leftrightarrow x\left(x^2+x-2\right)=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+2\right)=0\Leftrightarrow x=0;x=1;x=-2\left(ktm\right)\)
Vậy tập nghiệm của phương trình là S = { 0 ; 1 }
d, đưa về dạng hđt
Bài 2 : làm tương tự, chỉ khác ở chỗ mẫu số phức tạp hơn tí thôi
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a) (2x – 1)(4x2 + 2x + 1) – 4x(2x2 – 3) = 23
⇔ 8x3 – 1 – 8x3 + 12x = 23
⇔ 12x = 24 ⇔ x = 2.
Tập nghiệm của phương trình: S = {2}
b) ĐKXĐ : x + 1 ≠ 0 và x – 2 ≠ 0 (vì vậy x2 – x – 2 = (x + 1)(x – 2) ≠ 0)
⇔ x ≠ -1 và x ≠ 2
Quy đồng mẫu thức hai vế :
Khử mẫu, ta được : x2 – 4 – x – 1 = x2 – x – 2 – 3 ⇔ 0x = 0
Phương trình này luôn nghiệm đúng với mọi x ≠ -1 và x ≠ 2.
![](https://rs.olm.vn/images/avt/0.png?1311)
a, đk : x khác 5;-6
\(x^2+12x+36+x^2-10x+25=2x^2+23x+61\)
\(\Leftrightarrow2x+61=23x+61\Leftrightarrow21x=0\Leftrightarrow x=0\)(tm)
b, đk : x khác 1;3
\(x^2+2x-15=x^2-1-8\Leftrightarrow2x-15=-9\Leftrightarrow x=3\left(ktmđk\right)\)
pt vô nghiệm
a, đk : x khác 5;-6
x2+12x+36+x2−10x+25=2x2+23x+61x2+12x+36+x2−10x+25=2x2+23x+61
⇔2x+61=23x+61⇔21x=0⇔x=0⇔2x+61=23x+61⇔21x=0⇔x=0(tm)
b, đk : x khác 1;3
x2+2x−15=x2−1−8⇔2x−15=−9⇔x=3(ktmđk)x2+2x−15=x2−1−8⇔2x−15=−9⇔x=3(ktmđk)
pt vô nghiệm
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a) \(\sqrt {11{x^2} - 14x - 12} = \sqrt {3{x^2} + 4x - 7} \)
\(\begin{array}{l} \Rightarrow 11{x^2} - 14x - 12 = 3{x^2} + 4x - 7\\ \Rightarrow 8{x^2} - 18x - 5 = 0\end{array}\)
\( \Rightarrow x = - \frac{1}{4}\) và \(x = \frac{5}{2}\)
Thay nghiệm vừa tìm được vào phương trình \(\sqrt {11{x^2} - 14x - 12} = \sqrt {3{x^2} + 4x - 7} \) ta thấy chỉ có nghiệm \(x = \frac{5}{2}\) thảo mãn phương trình
Vậy nhiệm của phương trình đã cho là \(x = \frac{5}{2}\)
b) \(\sqrt {{x^2} + x - 42} = \sqrt {2x - 30} \)
\(\begin{array}{l} \Rightarrow {x^2} + x - 42 = 2x - 3\\ \Rightarrow {x^2} - x - 12 = 0\end{array}\)
\( \Rightarrow x = - 3\) và \(x = 4\)
Thay vào phương trình \(\sqrt {{x^2} + x - 42} = \sqrt {2x - 30} \) ta thấy không có nghiệm nào thỏa mãn
Vậy phương trình đã cho vô nghiệm
c) \(2\sqrt {{x^2} - x - 1} = \sqrt {{x^2} + 2x + 5} \)
\(\begin{array}{l} \Rightarrow 4.\left( {{x^2} - x - 1} \right) = {x^2} + 2x + 5\\ \Rightarrow 3{x^2} - 6x - 9 = 0\end{array}\)
\( \Rightarrow x = - 1\) và \(x = 3\)
Thay hai nghiệm trên vào phương trình \(2\sqrt {{x^2} - x - 1} = \sqrt {{x^2} + 2x + 5} \) ta thấy cả hai nghiệm đếu thỏa mãn phương trình
Vậy nghiệm của phương trình \(2\sqrt {{x^2} - x - 1} = \sqrt {{x^2} + 2x + 5} \) là \(x = - 1\) và \(x = 3\)
d) \(3\sqrt {{x^2} + x - 1} - \sqrt {7{x^2} + 2x - 5} = 0\)
\(\begin{array}{l} \Rightarrow 3\sqrt {{x^2} + x - 1} = \sqrt {7{x^2} + 2x - 5} \\ \Rightarrow 9.\left( {{x^2} + x - 1} \right) = 7{x^2} + 2x - 5\\ \Rightarrow 2{x^2} + 7x - 4 = 0\end{array}\)
\( \Rightarrow x = - 4\) và \(x = \frac{1}{2}\)
Thay hai nghiệm trên vào phương trình \(3\sqrt {{x^2} + x - 1} - \sqrt {7{x^2} + 2x - 5} = 0\) ta thấy chỉ có nghiệm \(x = - 4\) thỏa mãn phương trình
Vậy nghiệm của phương trình trên là \(x = - 4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 4:
Giả sử điều cần chứng minh là đúng
\(\Rightarrow x=y\), thay vào điều kiện ở đề bài, ta được:
\(\sqrt{x+2014}+\sqrt{2015-x}-\sqrt{2014-x}=\sqrt{x+2014}+\sqrt{2015-x}-\sqrt{2014-x}\) (luôn đúng)
Vậy điều cần chứng minh là đúng
2) \(\sqrt{x^2-5x+4}+2\sqrt{x+5}=2\sqrt{x-4}+\sqrt{x^2+4x-5}\)
⇔ \(\sqrt{\left(x-4\right)\left(x-1\right)}-2\sqrt{x-4}+2\sqrt{x+5}-\sqrt{\left(x+5\right)\left(x-1\right)}=0\)
⇔ \(\sqrt{x-4}.\left(\sqrt{x-1}-2\right)-\sqrt{x+5}\left(\sqrt{x-1}-2\right)=0\)
⇔ \(\left(\sqrt{x-4}-\sqrt{x+5}\right)\left(\sqrt{x-1}-2\right)=0\)
⇔ \(\left[{}\begin{matrix}\sqrt{x-4}-\sqrt{x+5}=0\\\sqrt{x-1}-2=0\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}\sqrt{x-4}=\sqrt{x+5}\\\sqrt{x-1}=2\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}x\in\varnothing\\x=5\end{matrix}\right.\)
⇔ x = 5
Vậy S = {5}
Ta có : \(\dfrac{1}{3}\left(x-2\right)+\dfrac{1}{4}x\left(x-2\right)-\dfrac{1}{5}\left(x-2\right)=\dfrac{23}{30}\)
\(\Rightarrow20\left(x-2\right)+15x\left(x-2\right)-12\left(x-2\right)=46\)
\(\Leftrightarrow15x^2-30x+8x-16-46=0\)
\(\Leftrightarrow15x^2-22x-62=0\)
( Đến đây ra vô tỉ luôn : vvvv ; không biết đề này đúng chưa :vvv0
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này![](data:image/png;base64,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)
để soạn thảo câu hỏi chính xác nha :vvvv