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(1)
x²y + xy²
= xy(x + y)
= (√2 - 1)(√2 + 1)(√2 - 1 + √2 + 1)
= 2√2
(2)
1/x + 1/y
= (x + y)/(xy)
= (√2 - 1 + √2 + 1)/[(√2 - 1)(√2 + 1)]
= 2√2
x²y + xy²
= xy(x + y)
= (√2 - 1)(√2 + 1)(√2 - 1 + √2 + 1)
= 2√2
(2)
1/x + 1/y
= (x + y)/(xy)
= (√2 - 1 + √2 + 1)/[(√2 - 1)(√2 + 1)]
= 2√2
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