Question

Find the value of a and b if 5+2√3/7+4√3 = a- b √3

Answer 1

We have the expression $\frac{5+2 \sqrt{3}}{7+4 \sqrt{3} } = a - b \sqrt{3}$

On rationalizing and simplifying this expression we get:

[tex]11 - 6 \sqrt{3} = a - b\sqrt{3} Hence on equating the coefficients, we get[/tex]

$a = 11$

$b = \frac{-6 \sqrt{3} }{-\sqrt{3}} = +6$