Question

已知X+Y=1,XY=5分之一,求X的平方Y+XY的平方和（X的平方+1)（Y的平方+1）

Answer 1

x^2y+xy^2 = xy(x+y) = 1/5

(x^2+1)(y^2+1)

= (xy)^2 + x^2 + y^2 +1

= (xy)^2 + (x+y)^2 - 2xy + 1

= 1/25 + 1 - 2/5 + 1

= 41/25