Question

Hey solve the d'un pleaseeeee exam tomorrow

Answer 1

Refer to attachment

I hope it helps you

Answer 2

Given : x = (√2 - 1)/(√2 + 1).

On rationalizing, we get

$=> \frac{\sqrt{2} - 1}{\sqrt{2} + 1} * \frac{\sqrt{2} - 1}{\sqrt{2} - 1 }$

$= > \frac{(\sqrt{2} - 1)^2}{(\sqrt{2})^2 - (1)^2 }$

$= > \frac{2 + 1 - 2\sqrt{2}}{2 - 1}$

$= > 3 - 2\sqrt{2}$

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Given : y = (√2 + 1)/(√2 - 1).

On rationalizing, we get

$= > \frac{\sqrt{2} + 1 }{\sqrt{2} - 1} * \frac{\sqrt{2} + 1}{\sqrt{2} + 1}$

$= > \frac{(\sqrt{2} + 1)^2 }{(\sqrt{2})^2 - (1)^2}$

$= > \frac{2 + 1 + 2\sqrt{2}}{2 - 1}$

$= > 3 + 2\sqrt{2}$

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Now,

⇒ x^2 + 5xy + y^2

⇒ (x + y)^2 + 3xy

⇒ (3 - 2√2 + 3 + 2√2)^2 + 3(3 - 2√2)(3 + 2√2)

⇒ (6)^2 + 3 * [(3)^2 - (2√2)^2]

⇒ 36 + 3[9 - 8]

⇒ 36 + 3

⇒ 39.

Therefore, the value of x^2 + 5xy + y^2 = 39.

Hope it helps!