Question

Como se resuelve (3 − 7)² = 7[(x − 3) · (2x − 1) + x]

Answer 1

Respuesta:

$x=\frac{21+\sqrt{371}}{14},\:x=\frac{21-\sqrt{371}}{14}$

Explicación paso a paso:

$\left(3-7\right)^2=7\left(\left(x-3\right)\left(2x-1\right)+x\right)\\\\16=14x^2-42x+21\\\\14x^2-42x+21=16\\\\14x^2-42x+5=0\\\\x_{1,\:2}=\frac{-\left(-42\right)\pm \sqrt{\left(-42\right)^2-4\cdot \:14\cdot \:5}}{2\cdot \:14}\\\\x_{1,\:2}=\frac{-\left(-42\right)\pm \:2\sqrt{371}}{2\cdot \:14}\\\\x_1=\frac{-\left(-42\right)+2\sqrt{371}}{2\cdot \:14},\:x_2=\frac{-\left(-42\right)-2\sqrt{371}}{2\cdot \:14}\\\\x=\frac{21+\sqrt{371}}{14},\:x=\frac{21-\sqrt{371}}{14}$