Question

Решите тригонометрическое уравнение. Со всеми объяснениями:
2х^4+х^2(х+2)=3(х+2)^2

Answer 1

$2x^4 + x^2(x+2)=3(x+2)^2 2x^4 + x^3 + 2x^2 = 3(x + 2)^2 2x^4 + x^3 + 2x^2 = 3x^2 + 12x + 12 2x^4 + x^3 - x^2 - 12x - 12 = 0 (x - 2)(x + 1)(2x^2 + 3x + 6) = 0 x - 2 = 0 ; x + 1 = 0 ; 2x^2 + 3x + 6 = 0$
$x = 2 ; x = -1 ; x^2 + frac{3x}{2} + 3 = 0$
$x = 2 ; x = - 1 ; x^2 + frac{3x}{2} = - 3$
$x = 2 ; x = 1 ; x^2 + frac{3x}{2} + frac{9}{16} = - frac{39}{16}$
$x = 2 ; x = - 1 ; (x + frac{3}{4})^2 = - frac{39}{16}$
$x1 = 2 ; x2 = -1$