Question

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

Answer 1

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