∛(5x+7) - ∛(5x-12) = 1
замена
∛(5x+7) = m
∛(5x-12) = n
тогда
m - n = 1
m³ - n³ = 5x+7 - (5x-12) = 19
(m-n)(m² + mn + n²)=19
m² - 2mn + n² + 3mn = 19
(m-n)² + 3mn = 19
3mn = 18
mn = 6
m=n+1
n(n+1)-6=0
n²+n-6=0
D=1+24=25=5²
n12=(-1+-5)/2= -3 2
n=-3 m=-2
n=2 m =3
∛(5x+7) = m
∛(5x-12) = n
1. 5x+7=-8 5x=-15
5x-12=-27 5x=-15 x=-3
2. 5x+7=27 5x=20
5x-12=8 5x=20 x=4
ответ -3 и 4