Question

2%20%5Csqrt%7B3%7D%20%3D%20x%20%2B%20%20%5Csqrt%7B6y%7D%20%5C%3A%20find%20%5C%3A%20the%20%5C%3A%20value%20%5C%3A%20of%20%5C%3A%20x%20%5C%3A%20and%20%5C%3A%20y" id="TexFormula1" title="if \: \sqrt{2} + \sqrt{3} \div 3 \sqrt{2} - 2 \sqrt{3} = x + \sqrt{6y} \: find \: the \: value \: of \: x \: and \: y" alt="if \: \sqrt{2} + \sqrt{3} \div 3 \sqrt{2} - 2 \sqrt{3} = x + \sqrt{6y} \: find \: the \: value \: of \: x \: and \: y" align="absmiddle" class="latex-formula">
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Answer 1

Given info:- $\textsf{If (√3+√2)/(3√2-2√3) = x+y√6,}$

$\textsf{then find the value of x and y?}$

Explanation:-

$\textsf{Consider LHS=}$

$\rm \: \frac{ \sqrt{2 } + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} }$

$\rm \: = \frac{ \sqrt{2 } + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} }$

$= \rm \: \frac{( \sqrt{2 } + \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3} )}{(3 \sqrt{2} - 2 \sqrt{3})(3 \sqrt{2} + 2 \sqrt{3}) }$

$\rm \: = \frac{3 \sqrt{2 \times 2} + 2 \sqrt{3 \times 2} + 3 \sqrt{2 \times 3} + 2 \sqrt{3 \times 3} }{(3 \sqrt{2} {)}^{2} - (2 \sqrt{3} {)}^{2} }$

$\rm = \frac{3 \times 2 + 2 \sqrt{6} + 3 \sqrt{6} + 2 \times 3}{18 - 12}$

$\rm \: = \frac{12 + 5 \sqrt{6} }{6}$

$\rm \: = 2 + \frac{5}{6} \sqrt{6}$

$\rm \therefore \: 2 + \frac{5}{6} \sqrt{6} = x + y \sqrt{6}$

$\textsf{On, comparing with RHS we notice that:}$

$\textsf{the value of x = 2 and y = 5/6.}$

$\bf{Read more:}$

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