Question

please solve this asap. thankyou so much. may you be blessed ​

Answer 1

Tip:

If you're facing confusion, you can break the expression into "a – b" and then solve for 'a' followed by 'b'. After rationalising the denominator, then simplify the expression. The outcome will be the answer.

*This method will be a bit lengthy but easy.*

For e.g.,

Let,

$\frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } = a$ &

$\frac{ \sqrt{12} }{ \sqrt{3} - \sqrt{2} } = b$

Solving for a:-

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

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

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

$= \frac{18 - 12\sqrt{6} + 12}{18 - 12}$

$= \frac{30 - 12 \sqrt{6} }{6} = 5 - 2 \sqrt{6}$

NOW, solving for b:-

$\frac{ \sqrt{12} }{ \sqrt{3} - \sqrt{2} }$

$= \frac{2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} }$

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

$= 6 + 2 \sqrt{6}$

NOW, adding a and b:-

$( 5 - 2 \sqrt{6}) + (6 + 2 \sqrt{6})$

$= 11$ (Answer)