Question

已知(x+y)的二次方=17,(x-y)的二次方=13求(1)x的二次方+y的二次方(2)xy

Answer 1

(x+y)²=17，(x-y)²=13

x²+y²=[(x+y)²+(x-y)²]/2
=(17+13)/2
=15

xy=[(x+y)²-(x-y)²]/4
=(17-13)/4
=1

Answer 2

(x+y)²=x²+2xy+y²=17
(x-y)²=x²-2xy+y²=13

∵x²+2xy+y²+x²-2xy+y²=2x²+2y²=2(x²+y²)
∴x²+y²=(17+13)/2=15

∵x²+2xy+y²-x²+2xy-y²=4xy
∴xy=(17-13)/4=1