Question

If a = 8+√7
b = 1/9
find a^2+b^2​

Answer 1

Answer:

27/31

Step-by-step explanation:

a = √8 - √7 , a = 1/b = b = 1/a = {1/(√8-√7)}

=> b= (√8+√7)/{(√8)^2-(√7)^2} = √8 + √7.

So (a^2+b^2–3ab)/(a^2+ab+b^2)

= {(a-b)^2 - ab}/{a+b)^2-ab}. ……(1)

Now a+b = (√8-√7)+(√8+√7) = 2√8

a - b = (√8-√7)-(√8+√7)= -2√7

ab = (√8-√7)(√8+√7)= 8–7 = 1

Substituting these values in (1) we get

{(-2√7)^2 - 1}/{(2√8)^2–1) = (28–1)/(32–1)

= 27/31