Question

if x=5+ root 24 then find 10x^2+1/x^2-97x+1/x-10

Answer 1

Hi ,

It is given that ,

x = 5 + √24 ---( 1 )

x² = ( 5 + √24 )²

x² = 25 + 24 + 10√24

x² = 49 + 10√24 ---( 2 )

1/x = 1/( 5 + √24 )

= ( 5 - √24 )/[ (5 + √24 )( 5 - √24 ) ]

= ( 5 - √24 ) / [ 5² - ( √24 )² ]

= ( 5 - √24 ) / ( 25 - 24 )

1/x = 5 - √24 ----( 3 )

1/x² = ( 5 - √24 )²

= 25 + 24 - 10√24

1/x² = 49 - 10√24 ---( 4 )

Therefore ,

10x² + 1/x² - 97x + 1/x - 10

= 10(49+10√24)+(49-10√24)-97(5+√24)

+(5-√24)-10

= 490 + 100√24 + 49 - 10√24 - 485 - 97√24

+ 5 - √24 - 10

= 544 - 495 + 100√24 - 108√24

= 49 - 108√24

or

= 49 - 108 √ ( 4 × 6 )

= 49 - 108 × 2 √6


= 49 - 216√6

I hope this helps you..

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