Question

If (√3 + √2) /(√3 - √2) = a+b√6 then find a and b​

Answer 1

$\quad \ \ \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } = {\footnotesize{ a + b \sqrt{6} }}$

$\Rightarrow \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } = {\footnotesize{ a + b \sqrt{6} }}$

$\Rightarrow \frac{ {( \sqrt{3} + \sqrt{2} ) }^{2} }{ {( \sqrt{3}) }^{2} - {( \sqrt{2}) }^{2} } = {\footnotesize{ a + b \sqrt{6} }}$

$\Rightarrow \frac{ {( \sqrt{3}) }^{2} + {( \sqrt{2} )}^{2} + 2( \sqrt{3} )( \sqrt{2}) }{ {( \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} } = {\footnotesize{ a + b \sqrt{6} }}$

$\Rightarrow \frac{3 + 2 + 2 \sqrt{6} }{3 - 2} = {\footnotesize{ a + b \sqrt{6} }}$

$\Rightarrow \frac{5 + 2 \sqrt{6} }{1} = {\footnotesize{ a + b \sqrt{6} }}$

$\Rightarrow {\footnotesize{ 5 + 2 \sqrt{6} = a + b \sqrt{6} }}$

On comparing, we get :

• a = 5
• b = 2

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