Question

\(\left(4x-5\right)\left(4x+1\right)-4\left(x-1\right)\left(x+1\right)=7\)

Answer 1

Ta có:

\(\left(4x-5\right)\left(4x+1\right)-4\left(x-1\right)\left(x+1\right)=7\)

\(\Rightarrow16x^2-16x-5-4\left(x^2-1\right)=7\)

\(\Rightarrow16x^2-16x-5-4x^2+4=7\)

\(\Rightarrow12x^2-16x=8\)

\(\Rightarrow3x^2-4x=2\)

\(\Rightarrow3\left(x^2-2.\frac{2}{3}.x+\left(\frac{2}{3}\right)^2\right)=2\)

\(\Rightarrow\left(x-\frac{2}{3}\right)^2=\frac{2}{3}\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{2}{3}=\sqrt{\frac{2}{3}}\\x-\frac{2}{3}=-\sqrt{\frac{2}{3}}\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=\sqrt{\frac{2}{3}}+\frac{2}{3}\\x=\frac{2}{3}-\sqrt{\frac{2}{3}}\end{cases}}\)