Question

hey guys hepl me solve this question plzzz!!!​

Answer 1

Given :-

a = 3 - 2√2

So , 1/a = 1/(3 - 2√2)

=> 1 x (3 + 2√2) / (3 - 2√2)(3 + 2√2)

=> (3 + 2√2) / (3)² - (2√2)²

[ By identity :- (a + b)(a - b) = a² - b² ]

=> (3 + 2√2) / (9 - 8)

=> 3 + 2√2 / 1

=> 3 + 2√2

Now , let's subtitute the values of "a" and 1/a in (a² - 1/a²)

Substituting:-

(3 - 2√2)² - (3 + 2√2)²

=> (3)² + (2√2)² - 2 x 2√2 x 3 - { (3)² + (2√2)² + 2 x 3 x 2√2 }

[ By the identities :- (a + b)² = ( a² + b² + 2ab ) and

(a - b)² = ( a² + b² - 2ab ) ]

=> 9 + 8 - 12√2 - { 9 + 8 +12√2 }

=> 17 - 12√2 - 17 - 12√2

=> -12√2 - 12√2

=> -√2(12 + 12)

=> -√2(24)

=> -24√2

Solved.

Hope it helped you...