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Step-by-step explanation:
x+y=(√a+√b/√a-√b)+(√a-√b/√a+√b)
={(√a+√b)²+(√a-√b)²}/(√a)²-(√b)²
=a+2√ab+b+a-2√ab+b/a-b
=2(a+b)/a-b
xy=(√a+√b/√a-√b)(√a-√b/√a+√b)
xy=a-b/a-b
xy=1
x²+xy+y²=(x+y)²-xy
={2(a+b)/a-b}²-1
=4(a+b)²/(a-b)²-1
=4{(a²+2ab+b²)-(a²-2ab+b²)}/(a-b)²
=4(4ab)/(a-b)²
=16ab/(a-b)²
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