Question

If a =1-√7/1+√7 and b = 1+√7/1-√7 then find the value of a2+ab+b2/a2-ab+b2    ​

Answer 1

Answer:

Let(a2+b2−3ab)/a2+ab+b2=d/e

Given a= √8- √7

b=1/a = √8 +√7

Apply Componendo and dividendo

2a2+2b2−2ab)/−4ab=d+e/d−e

2(a2+b2−1)/−4=d+e/d−e

-(16+14–1)/2 = d+e/d-e

-29/2 = d+e/d-e

Again apply Componendo and dividendo

27/31= 2d/2e

d/e = 27/31

So,a2+b2−3ab/a2+ab+b2=27/31