Question

已知实数a,b满足ab=1,a+b=3,(1)求代数式a^2+b^2的值;(2)求a^4-b^4的值

Answer 1

a^2+b^2=(a+b)^2-2ab=3^2-2=7

(a-b)^2=a^2+b^2-2ab=7-2=5

a-b=±√5

a^4-b^4=(a^2+b^2)(a^2-b^2)=(a^2+b^2)(a-b)(a+b)=21(a-b)=±21√5