Question

9x+1=3(x²-5)-(x-3)(x-2)​

Answer 1

¡Hola!

Respuesta:

$Es\:x_1=1+2\sqrt{3},\:x_2=1-2\sqrt{3}$

Explicación paso a paso:

Utilizamos la fórmula de Segundo grado:

$\boxed{x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$

$9x+1=3\left(x^2-5\right)-\left(x-3\right)\left(x-2\right)\\\\9x+1=3x^2-15-x^2+5x-6\\\\9x+1=2x^2+5x-21\\\\2x^2+5x-22=9x\\\\2x^2-4x-22=0\\\\x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:2\left(-22\right)}}{2\cdot \:2}\\\\x_{1,\:2}=\frac{-\left(-4\right)\pm \:8\sqrt{3}}{2\cdot \:2}\\\\Se\:separan\:las\:soluciones:\\\\x_1=\frac{-\left(-4\right)+8\sqrt{3}}{2\cdot \:2},\:x_2=\frac{-\left(-4\right)-8\sqrt{3}}{2\cdot \:2}$

$x_1=\frac{4+8\sqrt{3}}{4},\:x_2=\frac{4-8\sqrt{3}}{4}\\\\x_1=1+2\sqrt{3},\:x_2=1-2\sqrt{3}$