Question

If = √7 − √5, find the value of ² + 1 ÷ a²

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Answer 1

the question is incomplete

Answer 2

20 - 3√35/2

Step-by-step explanation:

If a = √7 - √5

Then, value of a² + 1/a² = ?

As we know, (a+b)² = a² + 2ab + b²

So, (a+b)² - 2ab = a² + b² ______(1)

According to question, b = 1/a

Also, on Rationalising: 1/(√7 - √5)

= [1/(√7 - √5)]×[(√7 + √5)/(√7 + √5)]

= (√7 + √5)/[(√7 - √5)(√7 + √5)]

= (√7 + √5)/(7-5)

b = 1/a = (√7 + √5)/2

So, a² + 1/a² = (a + 1/a)² - 2a(1/a)

= [√7 - √5 + (√7 +√5)/2]² - 2

= ( 3√7/2 - √5/2)² - 2

= [(3√7/2)² + (√5/2)² - 2(3√7/2)(√5/2)] - 2

= 63/4 + 25/4 - 6√35/4 - 2

= 80/4 - 6√35/4

= 20 - 3√35/2

Thank you.