Question

I'll mark the best answer as brainliest Plz give step by step answer

Answer 1

Solution

Given :-

• x = (√2+1)/(√2-1) & y = (√2-1)/(√2+1)

Find :-

• Value of (x²+y²+xy)

Explanation

First , rationalize denominator of x

==> x = (√2+1)/(√2-1)

==> x = (√2+1)(√2+1)/(√2-1)(√2+1)

==>x = [(√2)²+1²+2*√2*1]/(√2²-1²)

==>x = (2+1+2√2)/(2-1)

==>x = (3+2√2)/1

==>x = (3+2√2)

Now, Calculate

==>x² = (3+2√2)²

==>x² = 3²+(2√2)²+2*3*2√2

==>x² = 9+8+12√2

==> x² = 17 + 12√2

Now, rationalize denominator of y

==>y = (√2-1)/(√2+1)

==>y = (√2-1)(√2-1)/(√2+1)(√2-1)

==>y = [(√2)²+1²-2*√2*1]/(√2²-1²)

==>y = (2+1-2√2)/(2-1)

==>y = (3-2√2)/(1)

==>y = (3-2√2)

So,Now

==>y² = (3-2√2)²

==>y² = 3²+(2√2)² - 2* 3 * (2√2)

==>y² = 9 + 8 - 12√2

==>y² = 17 - 12√2

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Now, Calculate (x²+y²+xy)

==> x²+y²+xy = (17+12√2)+(17-12√2)+(3+2√2)(3-2√2)

==>x²+y²+xy = 34 + [3² - (2√2)²]

==> x² + y² + xy = 34 + 9 - 8

==> x² + y² + xy = 35

Ans.

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