Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 889

³$$\sqrt{(65 + х)^2}$$ + 4³$$\sqrt{(65 - х)^2}$$ – 5³$$\sqrt{65^2 - x^2}$$ = 0

³$$\sqrt{(65 + х)^2}$$ + 4³$$\sqrt{(65 - х)^2}$$ – 5³$$\sqrt{(65 - x)(65 + x)}$$ = 0

Пусть m = ³$$\sqrt{65 + х}$$, n = ³$$\sqrt{65 - х}$$

m² + 4n² – 5mn = 0
m² + 4n² – 4mn – mn = 0
(m² – mn) + (4n² – 4mn) = 0
m(m – n) + 4n(n – m) = 0
m(m – n) – 4n(n – m) = 0
(m – n)(m – 4n) = 0
m – n = 0    или    m – 4n = 0
m = n                     m = 4n

1) если m = n
³$$\sqrt{65 + х}$$ = ³$$\sqrt{65 - х}$$
65 + x = 65 – x
2x = 0
X = 0

2) если m = 4n
³$$\sqrt{65 + х}$$ = 4 · ³$$\sqrt{65 - х}$$
³$$\sqrt{65 + х}$$ = ³$$\sqrt{64}$$ · ³$$\sqrt{65 - х}$$
³$$\sqrt{65 + х}$$ = ³$$\sqrt{64 · (65 - х)}$$
65 + x = 64 · (65 – x)
65 + x = 4160 – 64x
x + 64x = 4160 – 65
65x = 4095
x = 63

Ответ: 0 и 63