1.已知a+b=3ab=1,求a²+b²2.已知x+1÷x+4求x²+1÷x²3.已知（a+b-3）²+（ab+b）²+0,求（a-b）²4.已知（a+b）²=5（a-b）²=1,求a²+b²和a×b的值

Question

1.已知a+b=3 ab=1,求a²+b²
2.已知x+1÷x+4 求x²+1÷x²
3.已知（a+b-3）²+（ab+b）²+0,求（a-b）²
4.已知（a+b）²=5 （a-b）²=1,求a²+b²和a×b的值

Answer 1

1.a^2+b^2=(a+b)^2-2ab=3^2-2*1=7
2.x+1/x=4
(x+1/x)^2=x^2+1/x^2+2=4^2=16
x^2+1/x^2=16-2=14
3.(a+b-3)^2+(ab+b)^2=0
a+b-3=0
ab+b=0
b=0,a=3
或者a=-1,b=4
(a-b)^2=(3-0)^2=9
或者(a-b)^2=(-1-4)^2=25
4.a^2+b^2=[(a+b)^2+(a-b)^2]/2=(5+1)/2=3
ab=[(a+b)^2-(a-b)^2]/4=(5-1)/4=1