Question

if 2+√3/2-√3 = a+b√3 then find a & b

Answer 1

2+√3/2-√3
Rationalising denominator,
=2+√3/2-√3×2+√3/2+√3
=(2+√3)(2+√3)/(2-√3)(2+√3)
=(2+√3)²/(2²-√3²)
=[2²+√3²+2(2)(√3)]/4-3
=(4+3+4√3)/1
=7+4√3=a+b√3
Therefore, a=7 and b=4

Hope it helps

Answer 2

Hey there!

By rationalising we get,

2+√3(2+√3)/2-√3(2+√3)

= 2²+2(2)(√3)+√3² / 2²-√3²

= 4+4√3+3 / 4-3

= 7+4√3.

Comparing this with a+b√3, we get

7+4√3 = a+b√3

a = 7 and b = 4.

:)