Question

pls answer the question​

Answer 1

$N = \frac{\sqrt{\sqrt{5}+ 2} + \sqrt{\sqrt{5} - 2} }{\sqrt{\sqrt{5}+ 1}} - \sqrt{3 - 2\sqrt{2} } = 1$

Step-by-step explanation:

$N = \frac{\sqrt{\sqrt{5}+ 2} + \sqrt{\sqrt{5} - 2} }{\sqrt{\sqrt{5}+ 1}} - \sqrt{3 - 2\sqrt{2} }$

Now to simplify we will solve each term seperately

$\frac{\sqrt{\sqrt{5} + 2}}{\sqrt{\sqrt{5} + 1}} \times \frac{\sqrt{\sqrt{5} - 2}}{\sqrt{\sqrt{5} - 1}}$

= √ ( 5  - 2 + 2√5  - √5 ) /  (√(5 - 1)  

= √( 3 + √5) / √4

= √ ( 5/2 +  1/2  +  √5) / 2

= √ ( √(5/2)² + (1/√2)²  + 2(√(5/2))(1/√2) ) / 2

= √ ((√5 + 1) /√2 )² / 2

= ( √5 + 1 ) /2√2

$\frac{\sqrt{\sqrt{5} - 2}}{\sqrt{\sqrt{5} + 1}} \times \frac{\sqrt{\sqrt{5} - 1}}{\sqrt{\sqrt{5} - 1}}$

= √ ( 5 + 2 - 2√5  - √5 ) /  (√(5 - 1)  

= √( 7 - 3√5) / √4

= √ ( 5/2 +  9/2  -  3√5) / 2

= √ ( √(-5/2)² + (3/√2)²  + 2(√(-5/2))(3/√2) ) / 2

= √ ((3 - √5 ) /√2 )² / 2

= ( 3 - √5 ) /2√2

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

= √( 1  + 2  - 2√2)

= √( (-1)² + (√2)²  + 2(-1)(√2))

= √ (√2 - 1)²

= √2  - 1

( √5 + 1 ) /2√2  + ( 3 - √5 ) /2√2   -  (√2  - 1)

= 4/2√2 -  (√2  - 1)

= √2  - (√2  - 1)

= 1

=> N = 1

Learn More:

simplify 6-4√3|/6+4√3 by rationalizing the denominator

https://brainly.in/question/3963591

rationalise the denominator of 1/root 5+root6-root2 - Brainly.in

https://brainly.in/question/3740134

Answer 2

Answer:

, refer to the above attachment for the solution