Question

已知实数a,b满足a^2=2-2a,b^2=2-2b,且a不等于b,求b/a+a/b的值

Answer 1

由题意，a,b均为x^2=2-2x的根
则两根之和a+b=-2,两根之积ab=-2
将第一式两边平方得a^2+b^2+2ab=4,即工a^2+b^2=8
所以所求式子b/a+a/b=(a^2+b^2)/(ab)=8/(-2)=-4

Answer 2

a^2=2-2a,b^2=2-2b,且a不等于b,
所以a和b是方程x^2=2-2x的两个跟
x^2+2x-2=0
a+b=-2,ab=-2
a^2+b^2=(a+b)^2-2ab=8

b/a+a/b=(a^2+b^2)/ab=-4

Answer 3

a,b是方程x^2+2x-2=0的2个根
则a+b=-2
ab=-2

b/a+a/b=(a^2+b^2)/ab=(a+b)^2/ab-2=4/(-2)-2=-4

Answer 4

a,b为方程x^2+2x-2=0两根
a+b=-2,ab=-2
b/a+a/b=(a^2+b^2)/ab
=((a+b)^2-2ab)/ab
=-4