已知(a+b)^2=13,(a-b)^2=7,求1.a/b+b/a 2.a^4+b^4的值

(a+b)^2=13
所以a^2+2ab+b^2=13
所以a^2+b^2=13-2ab
(a-b)^2=7
所以a^2-2ab+b^2=7
所以a^2+b^2=7+2ab
所以13-2ab=7+2ab
ab=3/2
a^2+b^2=13-2ab=10

a/b+b/a=(a^2+b^2)/ab=10/(3/2)=15

a^4+b^4=(a^2+b^2)^2-2a^2b^2=(a^2+b^2)^2-2(ab)^2=10^2-2*(3/2)^2=191/2

(a+b)^2=13,(a-b)^2=7
(a+b)^2-(a-b)^2=13-7
(a+b+a-b)(a+b-a+b)=6
2a*2b=6
ab=3/2
a^2+b^2=(a+b)^2-2ab=13-3=10

1.a/b+b/a
=(a^2+b^2)/ab
=10*2/3
=20/3

2.a^4+b^4
=(a^2+b^2)^2-2a^2b^2
=100-2*9/4
=97+1/2

1.ab=[(a+b)^2-(a-b)^2]/4=3/2
a/b+b/a=[(a+b)^2-2ab]/ab=20/3
2.a^4+b^4=a^4+b^4+2a^2b^2-2a^2b^2
=(a^2+b^2)^2-2a^2b^2
=[(a/b+b/a)ab]^2-2(ab)^2
=100-9/2=95.5