Tìm x:

a) x(x + 4) – x²= 10

b) 5x²+ 2x = 0

c) x²– 16 = x + 4

d) (4x – 1)²– (x + 7)²= 0

Hướng dẫn giải

a) x(x + 4) – x²= 10

x²+ 4x – x²= 10

4x = 10

\(x = \frac{5}{2}\)

Vậy \(x = \frac{5}{2}\)

b) 5x²+ 2x = 0

x(5x + 2) = 0

\( \Rightarrow \left[ \begin{array}{l}x = 0\\5x + 2 = 0\end{array} \right.\)

\( \Rightarrow \left[ \begin{array}{l}x = 0\\x = \frac{{ - 2}}{5}\end{array} \right.\)

Vậy x = 0 và \(x = \frac{{ - 2}}{5}\).

c) x²– 16 = x + 4

(x + 4)(x – 4) – (x + 4) = 0

(x + 4)(x – 4 – 1) = 0

(x + 4)(x – 5) = 0

\( \Rightarrow \left[ \begin{array}{l}x + 4 = 0\\x - 5 = 0\end{array} \right.\)

\( \Rightarrow \left[ \begin{array}{l}x = - 4\\x = 5\end{array} \right.\)

Vậy x = 4 và x = 5.

d) (4x – 1)²– (x + 7)²= 0

(4x – 1 – x – 7)(4x – 1 + x + 7) =0

(3x – 8)(5x + 6) = 0

\( \Rightarrow \left[ \begin{array}{l}3x - 8 = 0\\5x + 6 = 0\end{array} \right.\)

\( \Rightarrow \left[ \begin{array}{l}x = \frac{8}{3}\\x = \frac{{ - 6}}{5}\end{array} \right.\)

Vậy \(x = \frac{8}{3}\) và \(x = \frac{{ - 6}}{5}\).