Question

if a=√3+√2 find the value of 1/a²​

Answer 1

Answer:

$a = \sqrt{3} + \sqrt{2} \\ \therefore \frac{1}{a} = \frac{1}{ \sqrt{3} + \sqrt{2}} \\ = \frac{1( \sqrt{3} - \sqrt{2}) }{( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2})} \\ = \frac{ \sqrt{3} - \sqrt{2} }{( \sqrt{3})^{2} - ({ \sqrt{2} )}^{2} } \\ = \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} \\ = \frac{ \sqrt{3} - \sqrt{2} }{1 } \\ = \sqrt{3} - \sqrt{2}$

$now \\ \frac{1}{ {a}^{2}} = ( \frac{1}{a})^{2} \\ = {( \sqrt{3} - \sqrt{2}) }^{2} \\ = ( \sqrt{3}) {}^{2} - 2 \times \sqrt{3} \times \sqrt{2} + {( \sqrt{2})}^{2} \\ = 3 - 2 \sqrt{6} + 2 \\ = 5 - 2 \sqrt{6}$