x-y=3,x^2+y^2=13 求xy和 x^4+y^4=

题目

x-y=3,x^2+y^2=13 求xy和 x^4+y^4=

答案

x-y=3,x^2+y^2=13
(x-y)^2=9
x^2-2xy+y^2=9
-2xy=9-(x^2+y^2)=9-13=-4
xy=2
x^4+y^4
=(x^2+y^2)^2-2(xy)^2
=13^2-2*2^2
=169-8
=161