Question

If a=2√2+√7 , then the value of a-1/a please tell me step by step​

Answer 1

Step-by-step explanation:

Given :-

a = 2√2+√7

To find :-

Find the value of a -(1/a) ?

Solution :-

Given that

a = 2√2+√7

=> a = √(2²×2)+√7

=> a = √(4×2)+√7

=> a = √8+√7

=> 1/a = 1/(√8+√7)

The denominator = √8+√7

The Rationalising factor of √8+√7 is √8-√7

On Rationalising the denominator then

=> 1/a = [1/(√8+√7]×[(√8-√7)/(√8-√7)]

=> 1/a = [1(√8-√7)]/[(√8+√7)(√8-√7)]

=> 1/a = (√8-√7)/[(√8+√7)(√8-√7)]

We know that

(a+b)(a-b) = a²-b²

Where a = √8 and b = √7

=> 1/a = (√8-√7)/[(√8)²-(√7)²]

=> 1/a = (√8-√7)/(8-7)

=> 1/a = (√8-√7)/1

=> 1/a = √8-√7

Now,

The value of a-(1/a)

= (√8+√7)-(√8-√7)

=> √8+√7-√8+√7

=> (√8-√8)+(√7+√7)

=> 0 +2√7

=> 2√7

Therefore, a-(1/a) = 2√7

Answer:-

The value of a-(1/a) for the given problem is 2√7

Used formulae:-

→ The Rationalising factor of√a+√b is √a-√b

→ (a+b)(a-b) = a²-b²