Question

Find the rational numbers a & b such that 2+5√7/2-5√7 = a+√7b

Answer 1

(2 + 5√7)/(2 – 5√7)
= [(2 + 5√7)/(2 – 5√7)] × [(2 + 5√7)/(2 + 5√7)]
= [ (4 + 175 + 20√7)/(4 – 175)]
= [(179 + 20√7)/(-171)]
= a + b√7
So, a = - 179/171
b = - 20/171

Answer 2

Answer:

(2 + 5√7)/(2 – 5√7)

= [(2 + 5√7)/(2 – 5√7)] × [(2 + 5√7)/(2 + 5√7)]

= [ (4 + 175 + 20√7)/(4 – 175)]

= [(179 + 20√7)/(-171)]

= a + b√7

which means a = - 179/171

b = - 20/171