Question

can anyone help me in this question please help me

Answer 1

√7 - 1/√7 + 1 - √7 + 1/√7 - 1 = a + b√7

First term: √7 - 1/√7 + 1

Rationalizing the denominator: √7 - 1*(√7 - 1)/√7 + 1*(√7 - 1)

= (√7 - 1)^2/(√7)^2 - (1)^2

= (√7)^2 - 2*√7*1 + (1)^2/7 - 1

= 7 - 2√7 + 1/6

= 8 - 2√7/6

Second term: √7 + 1/√7 - 1

Rationalizing the denominator: 7 + 1*(√7 + 1)/√7 - 1*(√7 + 1)

= (√7 + 1)^2/(√7)^2 - (1)^2

= (√7)^2 + 2*√7*1 + (1)^2/7 - 1

= 7 + 2√7 + 1/6

= 8 + 2√7/6

So now √7 - 1/√7 + 1 - √7 + 1/√7 - 1 = 8 - 2√7/6 - 8 + 2√7/6

= 0/6

= 0

So a = 0 and b = 0

Hope it helps :)