Question

If both a & b are rational number than find the value of a and b if
$\frac{5+2\sqrt{3} }{7+4\sqrt{3} } = a + b\sqrt{3}$

Answer 1

Answer:

a=11 and b=-6.

Step-by-step explanation:

$\frac{5 + 2\sqrt{3} }{7 + 4 \sqrt{3} } = \frac{5 + 2\sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4\sqrt{3} }{7 - 4\sqrt{3}} = \frac{(5 + 2\sqrt{3})(7 + 4 \sqrt{3})}{ {(7)}^{2} - {(4 \sqrt{3}) }^{2} } \\ \\ \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24}{49 - 48} = 11 - 6 \sqrt{3}$

on comparing 11-6√3 with a+b√3.

we get a=11 and b=-6.