Question

if x = √2-1/√2+2 and y = √2+1/√2-1 find x + y​

Answer 1

Answer:

$x = \frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1} \\ y = \frac{ \sqrt{2} + 1}{ \sqrt{2} - 1 } \\ x + y = \frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1 } + \frac{ \sqrt{2} + 1 }{ \sqrt{2} - 1} \\ = \frac{ {( \sqrt{2} - 1) }^{2} + {( \sqrt{2} + 1) }^{2} }{ {( \sqrt{2})}^{2} - {1}^{2} } \\ = \frac{2 + 1 - 2 \sqrt{2} + 2 + 1 + 2 \sqrt{2} }{2 - 1} \\ \frac{6}{1} \\ x + y = 6 \: \: \: \: ans$

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