Question

If x^2+1/x^2=66,find the value of x^3-1/x^3

Answer 1

$\bold {\huge{Ello!!}}$

$<b >Here's your answer$

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Given , x² + 1 / x² = 66

To find the value of : x³ - 1 / x³

Now , x² + 1 / x² = 66

=> ( x - 1 / x )² + 2. x. 1 / x = 66

[ • ( a )² + ( b )² = ( a - b )² + 2ab → Using this identity ]

=> ( x - 1 / x )² + 2 = 66

=> ( x - 1 / x )² = 66 - 2

=> ( x - 1 / x )² = 64

=> ( x - 1 / x )² = ( 8 )²

=> ( x - 1 / x ) = 8

Thus ,

x³ - 1 / x³

= ( x )³ - ( 1 / x )³

= ( x - 1 / x )³ + 3 . x . 1 / x ( x - 1 / x )

[ • ( a )³ - ( b )³ = ( a - b )³ + 3ab ( a - b ) → Using this identity ]

= ( 8 )³ + 3 × 8 [ • Putting the value of ( x - 1 / x ) ]

= 512 + 24

= 536 [ ★ Required answer ]

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$<b><u><marquee direction> Hope it helps !!$

Answer 2

Hye !!

Refer to the attachment please !!

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