Question

if a=3+√8 . then a2+1/a2=?

Answer 1

Step-by-step explanation:

a= 3 + √8

$\frac{1}{a} = \frac{1}{3 + \sqrt{8} }$

$= \frac{1}{3 + \sqrt{8} } \times \frac{3 - \sqrt{8} }{3 - \sqrt{8} } \: \: (rationalising \: the \: denominator)$

$= \frac{3 - \sqrt{8} }{(3 + \sqrt{8})(3 - \sqrt{8} ) }$

$= \frac{3 - \sqrt{8} }{( {3)}^{2} - ( { \sqrt{8}) }^{2} }$

$= \frac{3 - \sqrt{8} }{9 - 8}$

$= 3 - \sqrt{8}$

Therefore,

${a}^{2} + \frac{1}{ {a}^{2} } = ( {a + \frac{1}{a} )}^{2} - 2a \times \frac{1}{a}$

$= (3 + \sqrt{8} + 3 - \sqrt{8} ) - 2$

$= 6 - 2$

$= 4$

The value is 4.

Answer 2

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