Question

a+b√6=√8+√3/√8-√3 find the value of a and b
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Answer 1

$\huge\text{\underline{Answer}}$

$\bold\red{a = \frac{11}{5} , b = \frac{4}{5} }$

$\huge\sf\underline{Given}$

$\bold{a + b \sqrt{6} = \frac{ \sqrt{8} + \sqrt{3} }{ \sqrt{8} - \sqrt{3} }}$

Rationalise the denominator :-

$\implies$ $\bold{\frac{ \sqrt{8} + \sqrt{3} }{ \sqrt{8} - \sqrt{3} } \times \frac{ \sqrt{8} + \sqrt{3} }{ \sqrt{8} + \sqrt{3} } }$

$\implies$ $\bold{\frac{( { \sqrt{8} + \sqrt{3} ) }^{2} }{ 8 - 3} }$

$\implies$ $\bold{\frac{8 + 3 + 2 \times \sqrt{8} \times \sqrt{3} }{5} }$

$\implies$ $\bold{\frac{ 11 + 2 \sqrt{24} }{5}}$

$\implies$ $\bold{\frac{11}{5} + \frac{4 \sqrt{6} }{5} }$

By comparing with a + b √6 we get,

$\implies$ $\bold</strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong> a = \frac{11}{5} </strong><strong>,</strong><strong> </strong><strong>b = \frac{4}{5} </strong><strong>}$