Question

if x-1/x=7 find the value of x3-1/x3

Answer 1

Answer:

Hi ,

It is given that ,

x + 1/x = 7 -----( 1 )

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We know the algebraic identity,

a³ + b³ + 3ab ( a + b ) = ( a + b )³

Or

a³ + b³ = ( a + b )³ - 3ab( a + b )

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x³ + 1/x³ = (x + 1/x )³- 3 × x ×1/x(x + 1/x )

= ( x + 1/x )³ - 3( x + 1/x )

= 7³ - 3 × 7

= 7( 7² - 3 )

= 7 ( 49 - 3 )

= 7 × 46

= 322

I hope this helps you.

: )

Answer 2

$given \: \: \: x - \frac{1}{x} = 7 \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = ( {x - \frac{1}{x} })^{3} + 3(x - \frac{1}{x} ) \\ = {7}^{3} + 3 \times 21 \\ = 343 + 21 \\ = 364$