Question

If x = 1/3-x and x ≠ 3,find x³+1/x³

Answer 1

Question :

If x = 1/(3 - x) and x≠3 , then find the value of : x^3 + 1/x^3

Solution:

We have;

=> x = 1/(3 - x)

=> x(3 - x) = 1

=> 3 - x = 1/x

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

We know that;

(a + b)^2 = a^2 + b^2 + 2•a•b

Thus;

=> (x + 1/x)^2 = x^2 + 1/x^2 + 2•x•(1/x)

=> (3)^2 = x^2 + 1/x^2 + 2

=> 9 = x^2 + 1/x^2 + 2

=> x^2 + 1/x^2 = 9 - 2

=> x^2 + 1/x^2 = 7 -------(2)

Also,

We know that;

a^3 + b^3 = (a + b)(a^2 + b^2 - a•b)

Thus;

x^3 + 1/x^3

= (x + 1/x)[x^2 + 1/x^2 - x•(1/x)]

= 3•(7 - 1)

= 3•6

= 18

Hence,

The required value of x^3 + 1/x^3 is 18.

Answer 2

Hope this helps and thank you