Tìm x, biết: (4x – 1)^2 – (x + 7)^2 = 0

Câu 50: Tìm x, biết: (4x – 1)² – (x + 7)² = 0.

Trả lời

(4x – 1)² – (x + 7)² = 0

⇔ (4x – 1 – x – 7)(4x – 1 + x + 7) = 0

⇔ (3x – 8)(5x + 6) = 0

$$\begin{gathered} \iff \left[\begin{array}{l}3x-8=0\\ 5x+6=0\end{array}\right. \\ \iff \left[\begin{array}{l}x=\frac{8}{3}\\ x=-\frac{6}{5}\end{array}\right. \end{gathered}$$

Vậy $x\in \left\{\frac{8}{3};-\frac{6}{5}\right\}$ .