Question

If N= √(3+2√2) +√(3-2√2) / (√√3+1) - 2√√3-1 then value of N ​

Answer 1

Given :- if N = [√(3 + 2√2) + √(3 - 2√2)] / [√(3 + 2√2) - √(3 - 2√2)]

To Find :-

• Value of N ?

Answer :-

→ N = [√(3 + 2√2) + √(3 - 2√2)] / [√(3 + 2√2) - √(3 - 2√2)]

solving Numerator parts ,

→ √(3 + 2√2) + √(3 - 2√2)

→ √(3 + 2√2) = √{(1)² + (√2)² + 2 * 1 * √2}

using a² + b² + 2ab = (a + b)²

→ √(√2 + 1)²

→ (√2 + 1)

similarly,

→ √(3 - 2√2) = √{(1)² + (√2)² - 2 * 1 * √2}

using a² + b² - 2ab = (a - b)²

→ √(√2 - 1)²

→ (√2 - 1)

also, Putting these values in denominator also,

→ N = [√(3 + 2√2) + √(3 - 2√2)] / [√(3 + 2√2) - √(3 - 2√2)]

→ N = (√2 + 1 + √2 - 1)/(√2 + 1 - √2 + 1)

→ N = (2√2/2)

→ N = √2 (Ans.)

if we used , (1 + √2) and (1 - √2) values ,

→ N = (1 + √2 + 1 - √2) / (1 + √2 - 1 + √2)

→ N = 2/2√2

→ N = (1/√2) (Ans.)

Learn more :-

(7sqrt(3))/(sqrt(10+sqrt(3)))-(2sqrt(5))/(sqrt(6)+sqrt(5))-(3sqrt(2))/(sqrt(5)+3sqrt(2))

https://brainly.in/question/32043164

if the positive square root of (√190 +√ 80) i multiplied by (√2-1) and the

product is raised to the power of four the re...

https://brainly.in/question/26618255