Question

. Factorise:

If x +


$\frac{1}{?x}$




= 3 , find x2

+

2

$\frac{1}{ {x}^{2} }$


​

Answer 1

_______

GIVEN,

_______

$= > x + \frac{1}{x} = 3$

_________

TO FIND,

_________

$= > x ^{2} + \frac{1}{x ^{2} }$

_________________

CONCEPT USED,

_________________

$= > (x + y) ^{2} = x ^{2} + 2xy + y ^{2}$

____________

SOLUTION,

____________

$= > x + \frac{1}{x} = 3 \\ \\ ........by \: squaring \: both \: side........ \\ \\ = > (x + \frac{1}{x} ) ^{2} = (3) ^{2} \\ \\ = > x ^{2} + 2 \times x \times \frac{1}{x} + (\frac{1}{x}) ^{2} = 9 \\ \\ ............... \: cancel \: x \: ................ \\ \\ = > x ^{2} + 2 + \frac{1}{x ^{2} } = 9 \\ \\ = > (x ^{2} + \frac{1}{x ^{2} } ) = 9 - 2 \\ \\ = > (x ^{2} + \frac{1}{ {x}^{2} } ) = 7$

_________________

FINAL ANSWER,

_________________

$= > x ^{2} + \frac{1}{x ^{2} } = 7$

hope it helps you........

please mark me as a brain list..........

I WILL FOLLOW YOU..........