Question

(x2+x+1)(x2+x+2)-12=10

Answer 1

(x2+x+1)(x2+x+2)-12=10

$\left(x\cdot \:2+x+1\right)\left(x\cdot \:2+x+2\right)-12 =\left(3x+1\right)\left(3x+2\right)-12 =9x^2+9x+2-12 =9x^2+9x-10$

$9x^2+9x-10=10$

$9x^2+9x-10-10=10-10$

$9x^2+9x-20=0$

$\frac{-9+\sqrt{9^2-4\cdot \:9\left(-20\right)}}{2\cdot \:9}$

$=\frac{-9+\sqrt{9^2+4\cdot \:9\cdot \:20}}{2\cdot \:9}$

$\sqrt{9^2+4\cdot \:9\cdot \:20} =\sqrt{81+4\cdot \:9\cdot \:20} =\sqrt{81+720}=\sqrt{801}$

$=\frac{-9+\sqrt{801}}{18}$

$\sqrt{801}=3\sqrt{89}$

$=\frac{-9+3\sqrt{89}}{18}$

$=\frac{-3+\sqrt{89}}{6}$

$\frac{-9-\sqrt{9^2-4\cdot \:9\left(-20\right)}}{2\cdot \:9}$

$\sqrt{9^2+4\cdot \:9\cdot \:20} =\sqrt{81+4\cdot \:9\cdot \:20} =\sqrt{81+720} =\sqrt{801}$

$=\frac{-9-\sqrt{801}}{2\cdot \:9}$

$=\frac{-9-3\sqrt{89}}{18}$

$=-\frac{3\left(3+\sqrt{89}\right)}{18}$

$=-\frac{3+\sqrt{89}}{6}$

$x=\frac{-3+\sqrt{89}}{6},\:x=-\frac{3+\sqrt{89}}{6}$

Sper că te-am ajutat!

Succes!