Question

7+4√3=x
find √x + 1/√x

Answer 1

Solution :

Given x = 7 + 4√3

=> √x = √(7 + 4√3)

= √( 7 + 2√6 )

= √( 6 + 1 + 2×√6×√1 )

= √( √6 + 1 )²

= √6 + 1 -----( 1 )

1/√x = 1/( √6 + 1 )

= ( √6 - 1 )/[ (√6 +1 )( √6 - 1 )]

= ( √6 -1 )/[ (√6)² - 1 ]

= (√6 -1 )/( 6 - 1 )

= ( √6 - 1 )/5 --- ( 2 )

Now

√x + 1/√x

= (1 ) + (2)

= √6 + 1 + ( √6 - 1 )/5

= [ 5( √6+1) + √6 - 1 ]/5

= (5√6+5+√6-1)/5

= ( 6√6 + 4 )/5

= (2/5)(3√6 + 2)

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