Question

If x =
$8 - \sqrt {60}$
Find the value of
$\sqrt{x} - \frac{2}{ \sqrt{x} }$

Answer 1

Hi ,

x = 8 - 2√15

√x =✓( 8 - √60)

= √[ 8 - 2√15 ]

= √ ( 5 + 3 - 2√15 )


= √[ (√5 )² + ( √3 )² - 2 × √5 × √3 ]

= √ ( √5 - √3)²

= ( √5 - √3 ) ---( 1 )

1/√x = 1/( √5 - √3 )

= ( √5 + √3 )/[( √5 - √3 )( √5 + √3 )]

= ( √5 + √3 )/[ ( √5 )² - ( √3 )² ]

= ( √5 + √3 )/( 5 - 3 )

= ( √5 + √3 )/2 ---( 2 )

Now ,

√x - 2/√x

= ( √5 - √3 ) - 2[( √5 + √3 )/2]

= √5 - √3 - ( √5 + √3 )

= √5 - √3 - √5 - √3

= - 2√3

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!


Thanks