Question

Help please ill increase points in the next question! i need detailed answer

Answer 1

Answer:

a = 5

b = 2

Step-by-step explanation:

Given: $\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} = a + b\sqrt{6}$

On rationalising :

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

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

=   $\frac{3 + 2\sqrt{6} + 2}{3-2}$       (According to  identity)  ($(a+b)^{2} = a^{2} + 2ab + b^{2}$) &

                                                                ($(a+b) (a-b) = a^{2} - b^{2}$)

=   $\frac{5+2\sqrt{6} }{1}$

=   $5 + 2\sqrt{6}$

Therefore a = 5   &   b = 6

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