Question

if x= √2+1/√2-1 and y = √2-1/√2+1 than find x^2+y^2+2xy

Answer 1

Answer :

Given,

x = (√2 + 1)/(√2 - 1) and y = (√2 - 1)/(√2 + 1)

Now, x + y

= (√2 + 1)/(√2 - 1) + (√2 - 1)/(√2 + 1)

= {(√2 + 1)(√2 + 1) + (√2 - 1)(√2 - 1)}/{(√2 - 1)(√2 + 1)}

= {(√2 + 1)² + (√2 - 1)²}/(2 - 1),
since (a + b)(a - b) = a² - b²

= (2 + 2√2 + 1 + 2 - 2√2 + 1)/1

= 6

Now,

x² + y² + 2xy

= (x + y)²

= 6²

= 36

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