3(2х² + 5х)² - (2х² + 5х + 1)² = 23
Пусть 2х² + 5х = t
3t^2 - (t + 1)^2 = 23
3t^2 - (t^2 + 2t + 1) - 23 = 0
3t^2 - t^2 - 2t - 1 - 23 = 0
2t^2 - 2t - 24 = 0 /:2
t^2 - t - 12 = 0
D = 1 + 48 = 49
t1 = ( 1 + 7)/2 = 8/2 = 4;
t2 = ( 1 - 7)/2 = - 6/2 = - 3
Обратная замена
2х² + 5х = 4
2х² + 5х - 4 = 0
D = 25 + 32 = 57
x₁ = ( - 5 + √57)/4
x₂ = ( - 5 - √57)/4
2x² + 5x = - 3
2x² + 5x + 3 = 0
D = 25 - 24 = 1
x₃ = ( - 5 + 1)/4 = - 4/4 = - 1
x₄ = ( - 5 - 1)/4 = - 6/4 = - 1,5