Question

If X +1/X =7;find the value of x³+1/x³

Answer 1

Given:

= > x + 1/x = 7

On cubing both sides, we get

= > (x + 1/x)^3 = (7)^3

= > x^3 +1/x^3 + 3 * x * 1/x(x + 1/x) = 343

= > x^3 + 1/x^3 + 3(7) = 343

= > x^3 + 1/x^3 + 21 = 343

= > x^3 + 1/x^3 = 322.


Therefore the value of x^3 + 1/x^3 = 322.



Hope this helps!

Answer 2

Hey !!!

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

we know that

( a + b ) ² - 2ab = a² + b²

similarly in this term

(x + 1/x )²- 2x×1/x = x² + 1/x²

7² - 2 = x² + 1/x²

47 = x² + 1/x² ----------2)

•°• (a + b )³ = (a + b ) ( a² + b² - ab)

similarly

x³ + 1/x³ = ( x + 1/x) (x² + 1/x² - x×1/x)

x³ + 1/x² = 7 (47 - 1)

[putting value from 1st and 2nd equation ]


x³ + 1/x³ = 7× 46

x³ + 1/x³ = 322 Answer ✔

______________________

Hope it helps you !!!

@Rajukumar111
$.$