Question

2 + 5 root 7 by 2 --5 root 7 is equal to a + b root 7 ​

Answer 1

Question:-

(2+5√7)/(2-5√7) = a+√7b. Find the value of a and b.

Solution:-

a+√7b=(2+5√7)/(2-5√7)

or, a+√7b=(2+5√7)(2+5√7)/(2-5√7)(2+5√7)

or, a+√7b={2²+2.2.5√7+(5√7)²}/{(2)²-(5√7)²}

or, a+√7b=(4+20√7+175)/(4-175)

or, a+√7b=(179+20√7)/(-171)

or, a+√7b=-179/171+(-20√7/171)

Equating both sides,

a=-179/171 and b=-20/171