Question

一数学因式分解题：已知a+b=3,ab=1,求a^7+b^7的值

Answer 1

因式分解比较麻烦,直接计算.

a^2+b^2=(a+b)^2-2ab=7

a^3+b^3=(a+b)(a^2-ab+b^2)=3*6=18

a^4+b^4=(a^2+b^2)^2-2a^2b^2=7^2-2=47

a^7+b^7=(a^3+b^3)(a^4+b^4)-a^3b^4-a^4b^3=18*47-a^3b^3(a+b)=847-3=844