Find the value of a :frac{5+2 sqrt{3}}{7+4 sq | vedclass

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(A) To solve the expression,we rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator,which is $

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$11$

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(A) To solve the expression,we rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator,which is $(7-4 \sqrt{3})$.$L.H.S. = \frac{5+2 \sqrt{3}}{7+4 \sqrt{3}} 	imes \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}$$= \frac{11 - 6 \sqrt{3}}{1} = 11 - 6 \sqrt{3}$Given that $11 - 6 \sqrt{3} = a - 6 \sqrt{3}$,by comparing both sides,we get $a = 11$.

Find the value of $a$ :
$\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-6 \sqrt{3}$

Similar Questions

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Find the value of $a$ :$\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-6 \sqrt{3}$