Math, asked by njonak123tum, 1 year ago

value of A and B
7 + 4√3 ÷ 5 + 2√3 =A + B√3

Answers

Answered by sushant2505
3
Hi...✌

Here is your answer...☺
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 \frac{7 + 4 \sqrt{3} }{5 + 2 \sqrt{3} } = A + B \sqrt{3} \\ \\ On \: rationalising \: LHS \\ we \: get \\ \\ LHS:\\\frac{7 + 4 \sqrt{3} }{5 + 2 \sqrt{3} } \times \frac{5 - 2 \sqrt{3} }{5 - 2 \sqrt{3} } \\ \\ = \frac{35 - 14 \sqrt{3} + 20 \sqrt{3} - 24 }{5^{2} - {(2 \sqrt{3} ) }^{2} } \\ \\ = \frac{11 + 6 \sqrt{3} }{25 - 12} = \frac{11 + 6 \sqrt{3} }{13} \\ \\ = \frac{11}{13} + \frac{6 \sqrt{3} }{13} \\ \\ Now \: comparinig \: LHS \: and \: RHS \\ \\ \frac{11}{13} + \frac{6 }{13} \sqrt{3} = A + B \sqrt{3} \\ \\ We \: get \\ \\ A = \frac{11}{1 3} \: and \: B = \frac{6}{13}

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