Question

(7x - 1)² = 4 ( 1 -2x )²

Answer 1

\(\left(7x-1\right)^2=4\left(1-2x\right)^2\)

=>\(\left(7x-1\right)^2=\left(4x-2\right)^2\)

=>\(\left(7x-1-4x+2\right)\left(7x-1+4x-2\right)=0\)

=>(3x+1)(11x-3)=0

=>\(\left[{}\begin{matrix}3x+1=0\\11x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=\dfrac{3}{11}\end{matrix}\right.\)

Answer 2

\(\Leftrightarrow49x^2-14x+1=4\left(1-4x+4x^2\right)=4-16x+16x^2\\ \Leftrightarrow49x^2-14x+1-4+16x-16x^2=0\\ \Leftrightarrow33x^2+2x-3=0\)

\(\Delta=2^2-4.33.-3=400>0\Rightarrow\) PT có 2 nghiệm phân biệt.

\(\left[{}\begin{matrix}x_1=\dfrac{-2+\sqrt{400}}{2.33}=\dfrac{3}{11}\\x_2=\dfrac{-2-\sqrt{400}}{2.33}=-\dfrac{1}{3}\end{matrix}\right.\)