Question

已知X=√7-√5，y=√7+√5，求x^2+xy+y^2的平方根

要过程

Answer 1

(x^2+xy+y^2)^2=[(x+y)^2-xy]^2
=[(2√7)^2-(√7-√5)(√7+√5)]^2
=(28-2)^2
=26^2
=676

Answer 2

x^2+xy+y^2=（X+Y)^2-Xy
=(√7-√5+√7+√5)^2-(√7-√5)(√7+√5)
=7-2=5

Answer 3

x^2+xy+y^2=(x+y)^2-xy=(2√7)^2-2=26