Question

Решите уравнение xx+4 + x+2x-4 = 32x^2-16

Answer 1

$frac{x(x-4)+(x+2)(x+4)}{(x-4)(x+4)} = frac{32}{ x^{2} -16} \ \ frac{ x^{2} -4x+ x^{2} +4x+2x+8}{ x^{2} -16} =frac{32}{ x^{2} -16} \ \ frac{2 x^{2} +2x+8}{ x^{2} -16} = frac{32}{ x^{2} -16} \ \ frac{2 x^{2} +2x+8-32}{ x^{2} -16} =0 \ \ x1 neq 4 \ \ x2 neq -4 \ \ 2 x^{2} +2x-24=0 \ \ x^{2} +x-12=0 \ \ D=1+48=49 \ \ sqrt{49} =7 \ \ x1=-1-7/2=-4 (ne- podxodit- po- usl )\ \ x2=-1+7/2=3 \ \ otvet:3$