Giải các phương trình sau: (Biến đổi đặc biệt)
a) \(\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}=10\)
b) \(\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}\)
K
Khách
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Những câu hỏi liên quan
4 tháng 2 2017
Phương trình 1:
\(\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}=10\)
\(\Rightarrow\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}-10=0\)
\(\Rightarrow\left(\frac{x-85}{15}-1\right)+\left(\frac{x-74}{13}-2\right)+\left(\frac{x-67}{11}-3\right)+\left(\frac{x-64}{9}-4\right)=0\)
\(\Rightarrow\frac{x-85-15}{15}+\frac{x-74-26}{13}+\frac{x-67-33}{11}+\frac{x-64-36}{9}=0\)
\(\Rightarrow\frac{x-100}{15}+\frac{x-100}{13}+\frac{x-100}{11}+\frac{x-100}{9}=0\)
\(\Rightarrow\left(x-100\right)\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)=0\)
Do \(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\ne0\)
\(\Rightarrow x-100=0\)
\(\Rightarrow x=100\)
Vậy x = 100.
4 tháng 2 2017
Phương trình 3:
\(\frac{1909-x}{91}+\frac{1907-x}{93}+\frac{1905-x}{95}+\frac{1903-x}{97}+4=0\)
\(\Rightarrow\left(\frac{1909-x}{91}+1\right)+\left(\frac{1907-x}{93}+1\right)+\left(\frac{1905-x}{95}+1\right)+\left(\frac{1903-x}{97}+1\right)=0\)
\(\Rightarrow\frac{1909-x+91}{91}+\frac{1907-x+93}{93}+\frac{1905-x+95}{95}+\frac{1903-x+97}{97}=0\)
\(\Rightarrow\frac{2000-x}{91}+\frac{2000-x}{93}+\frac{2000-x}{95}+\frac{2000-x}{97}=0\)
\(\Rightarrow\left(2000-x\right)\left(\frac{1}{91}+\frac{1}{93}+\frac{1}{95}+\frac{1}{97}\right)=0\)
Do \(\frac{1}{91}+\frac{1}{93}+\frac{1}{95}+\frac{1}{97}\ne0\)
\(\Rightarrow2000-x=0\)
\(\Rightarrow x=2000\)
Vậy x = 2000.
K
0
5 tháng 5 2020
Câu 1:
PT <=> \(\left(\frac{x-85}{15}-1\right)+\left(\frac{x-74}{13}-2\right)+\left(\frac{x-67}{11}-3\right)+\left(\frac{x-64}{9}-4\right)=0\)
<=> \(\frac{x-100}{15}+\frac{x-100}{13}+\frac{x-100}{11}+\frac{x-100}{9}=0\)
<=> \(\left(x-100\right)\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)=0\)
Mà \(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\ne0\)
<=> x - 100 = 0
<=> x = 100
Câu 2
PT <=> \(\left(\frac{x+2}{98}+1\right)+\left(\frac{x+4}{96}+1\right)=\left(\frac{x+6}{94}+1\right)+\left(\frac{x+8}{92}+1\right)\)
<=> \(\frac{x+100}{98}+\frac{x+100}{96}-\frac{x+100}{94}-\frac{x+100}{92}=0\)
<=> \(\left(x+100\right)\left(\frac{1}{98}+\frac{1}{96}-\frac{1}{94}-\frac{1}{92}\right)=0\)
Mà \(\frac{1}{98}+\frac{1}{96}-\frac{1}{94}-\frac{1}{92}\ne0\)
<=> x + 100 = 0
<=> x = -100
Câu 3:
PT <=> \(\left(\frac{x+2}{13}+1\right)+\left(\frac{2x+45}{15}-1\right)=\left(\frac{3x+8}{37}+1\right)+\left(\frac{4x+69}{9}-1\right)\)
<=> \(\frac{x+15}{13}+\frac{2\left(x+15\right)}{15}=\frac{3\left(x+15\right)}{37}+\frac{4\left(x+15\right)}{9}\)
<=> \(\left(x+15\right)\left(\frac{1}{13}+\frac{2}{15}-\frac{3}{37}-\frac{4}{9}\right)=0\)
mà \(\frac{1}{13}+\frac{2}{15}-\frac{3}{37}-\frac{4}{9}\ne0\)
<=> x+15 = 0
<=> x = -15
NV
Nguyễn Việt Lâm
Giáo viên
5 tháng 5 2020
1/
\(\Leftrightarrow\frac{x-85}{15}-1+\frac{x-74}{13}-2+\frac{x-67}{11}-3+\frac{x-64}{9}-4=0\)
\(\Leftrightarrow\frac{x-100}{15}+\frac{x-100}{13}+\frac{x-100}{11}+\frac{x-100}{9}=0\)
\(\Leftrightarrow\left(x-100\right)\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)=0\)
\(\Rightarrow x=100\)
2/
\(\frac{x+2}{98}+1+\frac{x+4}{96}+1-1-\frac{x+6}{94}-1-\frac{x+8}{92}=0\)
\(\Leftrightarrow\frac{x+100}{98}+\frac{x+100}{96}-\frac{x+100}{94}-\frac{x+100}{92}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{98}+\frac{1}{96}-\frac{1}{94}-\frac{1}{92}\right)=0\)
\(\Rightarrow x=-100\)
3/
\(\frac{x+2}{13}+1+\frac{2x+45}{15}-1-1-\frac{3x+8}{37}+1-\frac{4x+69}{9}=0\)
\(\Leftrightarrow\frac{x+15}{13}+\frac{2\left(x+15\right)}{15}-\frac{3\left(x+15\right)}{37}-\frac{4\left(x+15\right)}{9}=0\)
\(\Leftrightarrow\left(x+15\right)\left(\frac{1}{13}+\frac{2}{15}-\frac{3}{37}-\frac{4}{9}\right)=0\)
\(\Rightarrow x=-15\)
22 tháng 2 2020
1/
\(\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}\)
\(\Leftrightarrow\left(\frac{x-1}{13}-1\right)-\left(\frac{2x-13}{15}-1\right)=\left(\frac{3x-15}{27}-1\right)-\left(\frac{4x-27}{29}-1\right)\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}=\frac{3\left(x-14\right)}{27}-\frac{4\left(x-14\right)}{29}\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}-\frac{3\left(x-14\right)}{27}+\frac{4\left(x-14\right)}{29}=0\)
\(\Leftrightarrow\left(x-14\right)\left(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\right)=0\)
\(\Leftrightarrow x-14=0\)(vì 1/13 -2/15 -3/27 +4/29 khác 0)
\(\Leftrightarrow x=14\)
vậy...................
2/
\(a,ĐKXĐ:x\ne\pm2\)
\(b,A=\frac{4}{3x-6}-\frac{x}{x^2-4}\)
\(=\frac{4}{3\left(x-2\right)}-\frac{x}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{4\left(x+2\right)-3x}{3\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x+8}{3\left(x-2\right)\left(x+2\right)}\)
c,với \(x\ne\pm2\)ta có \(A=\frac{x+8}{3\left(x-2\right)\left(x+2\right)}\)
với x=1 thay vào A ta có \(A=\frac{1+8}{3\left(1-2\right)\left(1+2\right)}=\frac{9}{-9}=-1\)
19 tháng 4 2020
\(\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}\)
\(\Leftrightarrow\left(\frac{x-1}{13}-1\right)-\left(\frac{2x-13}{15}-1\right)=\left(\frac{3x-15}{27}-1\right)-\left(\frac{4x-27}{29}-1\right)\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}=\frac{3\left(x-14\right)}{27}-\frac{4\left(x-14\right)}{29}\)
\(\Leftrightarrow\left(x-14\right)\left(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\right)=0\)
<=> x-14=0
<=> x=14
NN
19 tháng 4 2020
\(\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}\)
\(\Leftrightarrow\frac{x-1}{13}-1-\frac{2x-13}{15}+1=\frac{3x-15}{27}-1-\frac{4x-27}{29}+1\)
\(\Leftrightarrow\left(\frac{x-1}{13}-1\right)-\left(\frac{2x-13}{15}-1\right)=\left(\frac{3x-15}{27}-1\right)-\left(\frac{4x-27}{29}-1\right)\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2x-28}{15}=\frac{3x-42}{27}-\frac{4x-56}{29}\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}=\frac{3\left(x-14\right)}{27}-\frac{4\left(x-14\right)}{29}\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}-\frac{3\left(x-14\right)}{27}+\frac{4\left(x-14\right)}{29}=0\)
\(\Leftrightarrow\left(x-14\right)\left(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\right)=0\)
Vì \(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\ne0\)
\(\Rightarrow x-14=0\)\(\Leftrightarrow x=14\)
Vậy tập nghiệm của phương trình là \(S=\left\{14\right\}\)
NK
0
22 tháng 2 2020
a, Ta có : \(\frac{x-10}{1994}+\frac{x-8}{1996}+\frac{x-6}{1998}+\frac{x-4}{2000}+\frac{x-2}{2002}=\frac{x-2002}{2}+\frac{x-2000}{4}+\frac{x-1998}{6}+\frac{x-1996}{8}+\frac{x-1994}{10}\)
=> \(\frac{x-10}{1994}-1+\frac{x-8}{1996}-1+\frac{x-6}{1998}-1+\frac{x-4}{2000}-1+\frac{x-2}{2002}-1=\frac{x-2002}{2}-1+\frac{x-2000}{4}-1+\frac{x-1998}{6}-1+\frac{x-1996}{8}-1+\frac{x-1994}{10}-1\)
=> \(\frac{x-2004}{1994}+\frac{x-2004}{1996}+\frac{x-2004}{1998}+\frac{x-2004}{2000}\frac{x-2004}{2002}=\frac{x-2004}{2}+\frac{x-2004}{4}+\frac{x-2004}{6}+\frac{x-2004}{8}+\frac{x-2004}{10}\)
=> \(\frac{x-2004}{1994}+\frac{x-2004}{1996}+\frac{x-2004}{1998}+\frac{x-2004}{2000}\frac{x-2004}{2002}-\frac{x-2004}{2}-\frac{x-2004}{4}-\frac{x-2004}{6}-\frac{x-2004}{8}-\frac{x-2004}{10}=0\)
=> \(\left(x-2004\right)\left(\frac{1}{1994}+\frac{1}{1996}+\frac{1}{1998}+\frac{1}{2000}+\frac{1}{2002}-\frac{1}{2}-\frac{1}{4}-\frac{1}{6}-\frac{1}{8}-\frac{1}{10}=0\right)\)
=> \(x-2004=0\)
=> \(x=2004\)
Vậy phương trình có nghiệm là x = 2004 .
b, Ta có : \(\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}=10\)
=> \(\frac{x-85}{15}-1+\frac{x-74}{13}-2+\frac{x-67}{11}-3+\frac{x-64}{9}-4=10-1-2-3-4=0\)
=> \(\frac{x-100}{15}+\frac{x-100}{13}+\frac{x-100}{11}+\frac{x-100}{9}=0\)
=> \(\left(x-100\right)\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)=0\)
=> \(x-100=0\)
=> \(x=100\)
Vậy phương trình có nghiệm là x = 100 .
thanks
16 tháng 4 2020
a, \(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}+\frac{x+7}{29}\)
\(\frac{x+36}{35}+\frac{x+36}{33}-\frac{x+36}{31}-\frac{x+36}{29}=0\)
\(\left(x+36\right)\left(\frac{1}{35}+\frac{1}{33}-\frac{1}{31}-\frac{1}{29}\right)=0\)
\(=>x+36=0\)
\(=>x=36\)
PN
31 tháng 1 2016
\(\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}=10\)
\(\Leftrightarrow\) \(\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}-10=0\)
\(\Leftrightarrow\) \(\left(\frac{x-85}{15}-1\right)+\left(\frac{x-74}{13}-2\right)+\left(\frac{x-67}{11}-3\right)+\left(\frac{x-64}{9}-4\right)=0\)
\(\Leftrightarrow\) \(\frac{x-100}{15}+\frac{x-100}{13}+\frac{x-100}{11}+\frac{x-100}{9}=0\)
\(\Leftrightarrow\) \(\left(x-100\right)\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)=0\) \(\left(\text{ *}\right)\)
Vì \(\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)\ne0\) nên từ \(\left(\text{ *}\right)\) \(\Rightarrow\) \(x-100=0\) \(\Leftrightarrow\) \(x=100\)
Vậy, tập nghiệm của pt là \(S=\left\{100\right\}\)
PN
31 tháng 1 2016
Mình giải rồi nhưng mạng gặp sự cố nên lời giải chắc mất rồi
a)\(\Leftrightarrow\left(x-100\right)\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)=0\)(Trừ từng số hạng cho 1;2;3;4 rồi nhóm)
Vậy x=100.
b)\(\Leftrightarrow\left(x-14\right)\left(\frac{1}{13}-\frac{1}{15}-\frac{1}{27}+\frac{1}{29}\right)=0\)(Trừ từng số cho 1)
Vậy x=14.