Question

If 5+3root/7+4root 3=a+b root3 then the value of a+b

Answer 1

Explanation:

$\frac{5 + \sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3}$

$\frac{(5 + \sqrt{3})(7 - 4 \sqrt{3})}{(7 + 4 \sqrt{3})(7 - 4 \sqrt{3}) } = a + b \sqrt{3}$

$\frac{28 - 20 \sqrt{3} + 7 \sqrt{3} - 12 }{ {(7)}^{2} - {(4 \sqrt{3}) }^{2} } = a + b \sqrt{3}$

$\frac{16 - 13 \sqrt{3} }{49 - 48} = a + b \sqrt{3}$

$16 + (- 13 \sqrt{3}) = a + b \sqrt{3}$

On comparing , we get a = 16 and b = -13

Therefore, the value of a + b = 3

I hope it helps you. If you have any doubts, then don't hesitate to ask.