Question

√3+√2÷√3-√2= a + b √6, then (a, b) =

a) (5,2)
b) (2,5)
c) (3, 2)
d) (1,5)​

Answer 1

$\underline{ \rm \red{solution}}$

$: \implies \rm \: \dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } = a + b \sqrt{6}$

$\underline{\rm \: \green{now \: \: \: rationalization \: \: the \: denominator}}$

$: \implies \rm \: \dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

$\underline{ \rm \blue{using \: this \: identities}}$

$\rm \: \to \: (a + b)(a - b) = ( {a}^{2} + {b}^{2} )$

$\rm \to \: (a + b)^{2} = {a}^{2} + {b}^{2} + 2ab$

$\underline{ \orange{\rm now \: take \: }}$

$: \implies \rm \: \dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

$\rm : \implies \: \dfrac{( \sqrt{3} + \sqrt{2} )^{2} }{( \sqrt{3} ) {}^{2} - ( \sqrt{2})^{2} }$

$\rm : \implies \: \dfrac{( \sqrt{3}) {}^{2} + ( \sqrt{2}) {}^{2} + 2 \times \sqrt{3} \times \sqrt{2} }{3 - 2}$

$\rm : \implies \dfrac{3 + 2 + 2 \sqrt{6} }{1}$

$: \implies \: 5 + 2 \sqrt{6}$

$\red{\rm \: answer}$

$\rm \to \: a = 5 \: \: and \: b \: = 2$

Answer 2

Answer:

answer

a=5andb=2

please mark me as brainlist