Question

这道题的最后一小题怎么做啊？

Answer 1

(a+b)^2=a^2+2ab+b^2=9/4
已知a^2+b^2=5/4
算出ab=1/2
(a^2+b^2)^2=a^4+2(ab)^2+b^4=25/16
算出a^4+b^4=25/16-2×（1/2)^2=17/16
(a^4+b^4)^2=a^8+2(ab)^4+b^8=625/256
算出a^8+b^8=625/256-2×（1/2)^4=593/256

Answer 2

1),=a³+b³
2），=a³-b³
∵(a+b)²=9/4,
∴a²+b²+2ab=9/4
∴2ab=9/4-(a²+b²)=9/4-5/4=1
∴ab=1/2,
①=（a+b）²=9/4,
②=(a+b)(a²-ab+b²)=3/2(5/4-1/2)9/8
③a^8+b^8=(a²)³+(b²)³=(a²+b²)(a^4-(ab)²+b^4)
=(a²+b²)[(a²+b²)²-3(ab)²]
=5/4[(5/4)²-3x1/4]
=65/64