Question

Hey friends!
solve it urgent wrong answer will be reported. ​

Answer 1

EXPLANATION.

$\sf \implies N = \dfrac{\sqrt{\sqrt{5}+ 2 }+ \sqrt{\sqrt{5} - 2} }{\sqrt{\sqrt{5}+ 1} } - \sqrt{3 - 2\sqrt{2} }$

As we know that,

Let us assume that,

⇒ x = √√5 + 2 + √√5 - 2.

Square on both sides, we get.

⇒ x² = (√√5 + 2 + √√5 - 2)².

⇒ x² = (√√5 + 2)² + (√√5 - 2)² + 2(√√5 + 2)(√√5 - 2).

⇒ x² = √5 + 2 + √5 - 2 + 2((√5)² - (2)²).

⇒ x² = 2√5 + 2(5 - 4).

⇒ x² = 2√5 + 2.

⇒ x² = 2(√5 + 1.

⇒ x = √2√√5 + 1.

As we know that,

Assume,

⇒ y = √3 - 2√2.

We can write the equation, as.

⇒ y = √(1)² + (√2)² - 2√2.

As we know that,

Formula of (a - b)² = a² + b² - 2ab.

using this formula on equation, we get.

⇒ y = √(√2 - 1)².

⇒ y = √2 - 1.

⇒ N = x/√√5 + 1 - y.

⇒ N = √2(√√5 + 1)/√√5 + 1 - (√2 - 1).

⇒ N = √2 - (√2 - 1).

⇒ N = √2 - √2 + 1.

⇒ N = 1.