Question

If
$(x - \frac{1}{x} ) = \frac{1}{2}$
find the value of
$(4x {}^{2} + \frac{4}{x {}^{2} } )$
with steps

Answer 1

                              ======================

Given,

⇒ { x - ( 1/x ) } = 1/2

By squaring both sides,

⇒ { x - ( 1/x ) }² = ( 1/2 )²

⇒ { x² + ( 1/x² ) - 2 × x × ( 1/x ) } = ( 1/4 )

⇒ { x² + ( 1/x² ) - 2 } = ( 1/4 )

⇒ x² + ( 1/x² ) = ( 1/4 ) + 2

⇒ x² + ( 1/x² ) = ( 1 + 8 ) / 4

⇒ x² + ( 1/x² ) = 9/4.  ------ ( 1 ).

Now,

= { 4x² + ( 4/x² ) }

By takinh 4 as common,

= 4 { x² + ( 1/x² ) }

Now by substituting the value of ( 1 ),

= 4 ( 9/4 )

= 9.

The required answer is 9.


Hope it helps !!