Original formula = (√ x+√ y) 2 √ x √ (√ x+√ y) √ [y √ x+x √ y]

=(√x+√y)÷√x÷[(√x+√y)÷√xy]

=√y

Second:

x+√(2y)=√3 ①

y+√(2x)=√3，②

①-②: x-y+√2(√y-√x)=0。

Namely: √x+√y=√2 ③.

①-②: x+y+√2(√x+√y)=2√3。

(√x+√y)^2-2√xy+√2(√x+√y)=2√3 ④

③ Substituting into ④ gives: 2-2 √ xy+2 = 2 √ 3.

That is, √ xy = 2-√ 3 ⑤.

1÷√x+ 1÷√y =(√x+√y)÷√xy =√2÷(2-√3)

= 2√2+√6

I hope it helps you.

This problem is to add and subtract the values of √xy and √ x+√ y.