\(\left\{{}\begin{matrix}\dfrac{x+3}{x-2}=a\\\dfrac{x-3}{x+2}=b\end{matrix}\right.\)
\(pt\Leftrightarrow a^2+6b^2-7ab=0\)
\(\Leftrightarrow a^2-ab+6b^2-6ab=0\)
\(\Leftrightarrow a\left(a-b\right)-6b\left(a-b\right)=0\)
\(\Leftrightarrow\left(a-6b\right)\left(a-b\right)=0\Leftrightarrow\left[{}\begin{matrix}a=6b\\a=b\end{matrix}\right.\)
Tự full nhé bạn
Giải pt: \(\left(\frac{x+3}{x-2}\right)^2+6\left(\frac{x-3}{x+2}\right)^2=\frac{7\left(x^2-9\right)}{x^2-4}\)
Bài 3 : Giải các phương trình sau bằng cách đưa về dạng ax+b=0 :
a) \(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)
b) \(4\left(0,5-1,5x\right)=-\frac{5x-6}{3}\)
c) \(\frac{x+4}{5}-x+4=\frac{x}{3}-\frac{x-2}{2}\)
d) \(\frac{4x+3}{5}-\frac{6x-2}{7}=\frac{5x+4}{3}+3\)
e) \(\frac{1}{4}\left(x+3\right)=3-\frac{1}{2}\left(x+1\right)-\frac{1}{3}\left(x+2\right)\)
Giải phương trình (áp dụng phương pháp đặt ẩn phụ):
a) (x - 1)3 + x3 + (x + 1)3 = (x + 2)3
b) (6x + 7)2(3x + 4)(x + 1) = 6
c) \(8\left(x+\frac{1}{x}\right)^2+4\left(x^2+\frac{1}{x^2}\right)-4\left(x^2+\frac{1}{x^2}\right)\left(x+\frac{1}{x}\right)^2=\left(x+4\right)^2\)
Bài 3: Giải các phương trình sau bằng cách đưa về dạng ax+b =0 :
a) \(\frac{3x-11}{11}-\frac{x}{3}=\frac{3x-5}{7}-\frac{5x-3}{9}\)
b) \(\frac{9x-0,7}{4}-\frac{5x-1,5}{7}=\frac{7x-1,1}{6}-\frac{5\left(0,4-2x\right)}{5}\)
c) \(\frac{5\left(x-1\right)+2}{6}-\frac{7x-1}{4}=\frac{2\left(2x-1\right)}{7}-5\)
d) \(14\frac{1}{2}-\frac{2\left(x+3\right)}{5}=\frac{3x}{2}-\frac{2\left(x-7\right)}{3}\)
Giải các phương trình sau
a) \(\frac{1}{x+1}-\frac{5}{x-2}=\frac{15}{\left(x+1\right)\left(2-x\right)}\)
b) \(\frac{1}{2x-3}-\frac{3}{x\left(2x-3\right)}=\frac{5}{x}\)
c) \(\frac{6}{x-1}-\frac{4}{x-3}=\frac{8}{2x-6}\)
d) \(\frac{3}{\left(x-1\right)\left(x-2\right)}+\frac{2}{\left(x-3\right)\left(x-1\right)}=\frac{1}{\left(x-2\right)\left(x-3\right)}\)
e) \(\frac{1}{x-2}+\frac{5}{x+1}=\frac{3}{2-x}\)
f) \(\frac{5x}{2x+2}+1=-\frac{6}{x+1}\)
g) \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{4}{x^2-1}\)
h) \(\frac{3x}{x-2}-\frac{x}{x-5}=\frac{3x}{\left(x-2\right)\left(5-x\right)}\)
Giải các phương trình sau
e) \(\frac{1}{2}\left(x+1\right)+\frac{1}{4}\left(x+3\right)=3-\frac{1}{3}\left(x+2\right)\)
f)(4-3x)(10x-5)=0
g) (x-3)(2x-1)=(2x-1)(2x+3)
h) 9 - x^2 = 0
Giải các phương trình sau:
a) \(\left(\frac{x-2}{x-1}\right)^2-5\left(\frac{x+2}{x+1}\right)^2+4\left(\frac{x^2-4}{x^2-1}\right)=1\)
b) \(\left(\frac{x-1}{x}\right)^2+\left(\frac{x-1}{x-2}\right)^2=\frac{40}{9}\)
c) \(x.\frac{4-x}{x+2}.\left(\frac{8-2x}{x+2}\right)=3\)
d) \(\frac{1}{3x-2020}+\frac{1}{4x-2018}+\frac{1}{5x-2017}=\frac{1}{12x-2019}\)
Giải phương trình:
a) \(\frac{4x-8+\left(4-2x\right)}{x^2+1}=0\)
b) \(\frac{x^2\left(x-3\right)}{x}=0\)
c) \(\frac{\left(x+2\right)\left(2x-1\right)-x-2}{x^2-x+1}=0\)
Giải các phương trình sau bằng cách đưa về dạng ax + b = 0:
\(a,\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)
\(b,\frac{x+1}{3}+\frac{3\left(2x+1\right)}{4}=\frac{2x+3\left(x+1\right)}{6}+\frac{7+12x}{12}\)
