Question

x=4+√15 find x^3-1/x^3

Answer 1

Heya Gori!

Answer :-

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Given :-

x = ( 4 + √15 )

To find :-

The value of x³ - 1 / x³

Salutation :-

Given , x = ( 4 + √15 )

Then ,

1 / x = 1 / ( 4 + √15 )

= 1 / ( 4 + √15 ) × 1

= 1 / ( 4 + √15 ) × ( 4 - √15 ) / ( 4 - √15 )

= ( 4 - √15 ) / { ( 4 + √15 ) × ( 4 - √15 ) }

= ( 4 - √15 ) / ( 4 )² - ( √15 )²

[ • As we know , a² - b² = ( a + b ) ( a - b ) ]

= ( 4 - √15 ) / ( 16 - 15 )

= ( 4 - √15 ) / 1

= ( 4 - √15 )

So ,

x - 1 / x

= ( 4 + √15 ) - ( 4 - √15 )

= 4 + √15 - 4 + √15

= + 2√15

Therefore ,

x³ - 1 / x³

= ( x - 1 / x )³ + 3 × x × 1 / x ( x - 1 / x ) [ • Using identity ]

= ( 2√15 )³ + 3 × 2√15

= 8 × 15√15 + 6√15

= 120√15 + 6√15

= 126√15                     [ ★ Required answer ]

•°• The value of x³ - 1 / x³ is 126√15.

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Hope it helps you dear! :)

Answer 2

Step-by-step explanation:

this is a very simple answer it can help you a lot and it is solve my own self so I really hope its help you thank you