已知(a+b)^2=7,(a-b)^2=3 a^2+b^2的值 ab的值 a^8+b^8的值

∵(a+b)^2=7……………………………………………………①
,(a-b)^2=3 ……………………………………………………②
①+②得：a^2+b^2=5 …………………………………………………③
③代入①得：ab=1……………………………………………………④
把③和④代入a^8+b^8=a^4+b^4)²-2a^4b^4=[(a^2+b^2)²-2(ab)²]²-2(ab)^4=(5²-2)²-2=527

(a+b)^2=7,(a-b)^2=3
展开相加得
a^2+b^2=5
(a+b)^2=7=a^2+b^2+2ab
ab=1
a^4+b^4
=(^2+b^2)^2-2a^2b^2
=25-2
=23
a^8+b^8
=(a^4+b^4)^2-2a^4b^4
=23^2-2
=527

(a+b)^2=a^2+b^2+2ab=7
(a-b)^2=a^2+b^2-2ab=3
2(a^2+b^2)=10
a^2+b^2=5
ab=1
(a^2+b^2)^2=a^4+b^4+2a^2b^2=25
a^4+b^4=23
(a^4+b^4)^2=a^8+b^8+2a^4b^4=23^2=529
a^8+b^8=527

,(a-b)^2=3 (1)
(a+b)^2=7, (2)
(1)+(2)
2*(a^2+b^2)=10
a^2+b^2=5
(2)-(1)
4ab=4
ab=1
a^8+b^8=(a^4+b^4)^2-2a^4b^4=[(a^2+b^2)^2-2a^2b^2]^2-2=(5^2-2)^2-2=527

a^8+b^8=（a^4+b^4)*(a^4-b^4)
=[(a^2+b^2)^2-2a^2b^2]*(a^2+b^2)(a^2-b^2)
=[(a^2+b^2)^2-2a^2b^2]*(a^2+b^2)(a+b)(a-b)
剩下的你自己带数据进去就OK了