Пусть a+b=7, ab=2. Найдите:

A) a^3+b^3;

B) a^3*b^6+a^6*b^3;

C) a^4+b^4

A+b=7, ab=2

(a+b) ²=a²+2ab+b²=a²+b²+2·2=49

a²+b²=49-4=45

A) a^3+b^3 = (a+b) (a²-ab+b²) = 7· (45-2) = 7·43=301;

B) a^3*b^6+a^6*b^3=a³b³ (a³+b³) = 2³·301=8·301=2408;

C) a^4+b^4 (a²+b²) ²=a^4+2a²b²+b^4 = 45²

a^4+b^4 = 45²-2a²b²=2025-8=2017