Question

Find the value of a and b in the following
5+2V3/
7 +4V3
= a - bV3​

Answer 1

Answer:

a = 11

b = 6

Step-by-step explanation:

$\frac{5+2\sqrt{3} }{7+4\sqrt{3} } = a-b\sqrt{3}\\\\\\ so~first~we~will~rationalise~the~denominator\\\\\\=\frac{5+2\sqrt{3} }{7+4\sqrt{3} } * \frac{7-4\sqrt{3} }{7-4\sqrt{3} }\\\\\\= \frac{(5+2\sqrt{3})(7-4\sqrt{3} ) }{(7)^2-(4\sqrt{3})^2 }\\\\\\= \frac{35-20\sqrt{3}+14\sqrt{3}-(8*3)}{49-(16*3)}\\\\\\= \frac{35-6\sqrt{3}-24 }{49-48}\\\\\\= \frac{35-24-6\sqrt{3} }{1}\\\\= \frac{11-6\sqrt{3}}{1}\\\\\\= 11-6\sqrt{3}\\\\\\now~substitute~the~value\\11-6\sqrt{3} = a-b\sqrt{3}\\\\\\a = 11\\\\b = 6$

edit :  ' * 'symbol represents multiplication

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