Question

If 'a' and 'b' are ratio am numbers, find the value of 'a' and 'b'-
(5+2√3)÷(7+2√3)=a+b√3

Answer 1

Solution:-

given by:-

$\frac{(5 + 2 \sqrt{3} )}{(7 + 2 \sqrt{3}) } = a + b \sqrt{3} \\ \frac{(5 + 2 \sqrt{3)} }{(7 + 2 \sqrt{3}) } \times \frac{7 - 2 \sqrt{3} }{7 - 2 \sqrt{3} } \\ \frac{35 + 14 \sqrt{3} - 10 \sqrt{3} - 12}{49 - 12} \\( 23 + 4 \sqrt{3} ) \times \frac{1}{37} \\ \frac{23}{37} + \frac{4}{37} \sqrt{3} = a + b\sqrt{3} \\ a = \frac{23}{37} \\ b = \frac{4}{37} \\ i \: hope \: its \: help$