Question

If x+1/x=7,then find the value of x3+1/x3

Answer 1

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

Hey there!
Here's your solution :

We will be using the Identity of ( a + b) ³

Given,
x + 1/x = 7 .

Now,
Cubing on both sides,

( x + 1/x)³ = 7³

x³ + 1/x³ + 3x(1/x) ( x + 1/x) = 343

x³ + 1/x³ = 343 - 3 ( 7)

x³ + 1/x³ = 322

Hope helped!