Question

Tìm x

(2x-3)² - 2(x-1)(2x-3) + (x-1)²=0

Answer 1

Đặt 2x - 3 = a ; x - 1 = b. Khi đó biểu thức trở thành:
\(a^2-2ba+b^2=0\)
\(\Rightarrow\left(a-b\right)^2=0\)
\(\Rightarrow a-b=0\)
Thế lại vào ta có:
\(\left(2x-3\right)-\left(x-1\right)=0\)
\(\Rightarrow\left(2x-x\right)-\left(3-1\right)=0\)
\(\Rightarrow x-2=0\)
\(\Rightarrow x=2\)

Answer 2

\(\left(2x-3\right)^2-2\left(x-1\right)\left(2x-3\right)+\left(x-1\right)^2=0\)

\(\Rightarrow\left(\left(2x-3\right)-\left(x-1\right)\right)^2=0\)

\(\Rightarrow\left(2x-3-x+1\right)^2=0\)

\(\Rightarrow x-2=0\Rightarrow x=2\)