Question

已知a+b=1，a^2+b^2=2，求①a/b+b/a②求a^4+b^4

Answer 1

2ab=(a+b)²-(a²+b²)=1²-2=-1
则ab=-0.5
①a/b+b/a=a²/ab+b²/ab=(a²+b²)/ab=2/（-0.5）=-4
②a^4+b^4=(a²+b²)²-2a²b²=2²-2×(-0.5)²=4-0.5=3.5

Answer 2

因为a+b=1，所以2ab=(a+b)^2-(a^2+b^2)=1-2=-1，ab=-1/2
1.a/b+b/a=(a^2+b^2)/(ab)=2/(-1/2)=-4
2.a^4+b^4=(a^2+b^2)^2-2(ab)^2=4-2*(1/4)=4-1/2=7/2

Answer 3

(a+b)^2=a^2+b^2+2ab =>1=2+2ab =>ab=-1/2
(1) a/b +b/a =(a^2+b^2)/ab=2/(-1/2)=-4...ans
(2) (a^2+b^2)^2 =a^4+b^4+2a^2b^2 => 4=a^4+b^4 +2(1/4) =>a^4+b^4=3.5..ans

Answer 4

(a+b)^2=a^2+2ab+b^2=1
a^2+b^2=2
所以可得：ab=-1/2

①a/b+b/a
=(a^2+b^2)/ab
=2/(-1/2)
=-4

②求a^4+b^4
=(a^2+b^2)^2-2a^2b^2
=(2)^2-2(-1/2)^2
=7/2

Answer 5

a+b=1 两边平方 a^2+b^2+2ab=1 ab=-1/2
①a/b+b/a=(a^2+b^2)/ab=-4
②a^4+b^4=(a^2+b^2)^2-2(ab)^2=7/2