Verified answer

(a⁵ + b⁵)² = a¹⁰ + b¹⁰ + 2a⁵b⁵ = 9 ⇔ 2a⁵b⁵ = 9 - a¹⁰ - b¹⁰

a¹⁵ + b¹⁵ = (a⁵ + b⁵)(a¹⁰ - a⁵b⁵ + b¹⁰)  = 3*(a¹⁰ + b¹⁰ - 4,5 + 0,5a¹⁰ + 0,5b¹⁰) (1)

a¹⁵ + b¹⁵= 9 (2)

Из (1) и (2) получаем:

3(1,5a¹⁰ + 1,5b¹⁰ - 4,5) = 9

1,5a¹⁰ + 1,5b¹⁰ - 4,5 = 3

1,5a¹⁰ + 1,5b¹⁰ = 4,5 + 3

1,5a¹⁰ + 1,5b¹⁰ = 7,5

a¹⁰ + b¹⁰ = 5

Ответ: 5.