Question

find the value of a if 5+2root3 /7+4root3=a-6root3

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a - 6 \sqrt{3}$

On rationalizing the denominator we get :

$= \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} }$

Using the identity :

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

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


Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
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