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2x = √2 + 1 / √2 – 1
y = √2 – 1 / √2 + 1
find the value of x² + y²+xy = ?​

1 thought on “><br />2x = √2 + 1 / √2 – 1<br />y = √2 – 1 / √2 + 1 <br />find the value of x² + y²+xy = ?​”

1. Answer:

   I have got the answer is 35

   Step-by-step explanation:

   so we have,

   x = (√2 + 1) /(√2 – 1)

   or, x = (√2 + 1)(√2 + 1) / (√2 – 1)(√2 + 1)

   or, x = [(√2)² + (2 × √2 × 1) + (1)²] / [(√2)² – (1)²]

   or, x = [2 + 2√2 + 1] / [2 -1]

   or, x = [3 + 2√2] / 1

   or, x = 3 + 2√2

   y = (√2 – 1) / (√2 + 1)

   or, 1/y = (√2 + 1) / (√2 – 1)

   or, 1/y = 3 + 2√2

   or, y = 1/(3 + 2√2)

   or, y = (3 – 2√2) / (3 + 2√2)(3 – 2√2)

   or, y = (3 – 2√2) / [(3)² – (2√2)²]

   or, y = (3 – 2√2) / [9 – 8)

   or, y = 3 – 2√2

   (x × y) = [(√2 + 1) / (√2 – 1)] × [(√2 – 1)(√2 + 1)] = 1

   (x + y) = (3 + 2√2 + 3 – 2√2) = 6

   x² + y² + xy

   = (x + y)² – 2xy + xy

   = (6)² – (2 × 1) + 1

   = 36 – 2 + 1

   = 37 – 2

   = 35

   see this answer hope it will help you

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