Question

if x+1/x=3,evaluate x^3+1/x^3​

Answer 1

Given: x+1/x = 3

Cubing both sides

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

Now, using the formula ( a+b)^3

x^3 + 1/x^3 + 3× x × 1/x ( x+ 1/x) = 27

x^3 + 1/x^3 + 3 (x+1/x) = 27

x^3 + 1/x^3 + 3 (3) = 27

x^3 + 1/x^3 = 27-9

x^3 + 1/x^3 = 18

Answer 2

Step-by-step explanation:

$x + \frac{1}{x} = 3$

Then,

${x}^{3} + \frac{1}{ {x}^{3} } \\ = {(x + \frac{1}{x}) }^{3} - 3x \frac{1}{x} (x + \frac{1}{x} ) \\ = {3}^{3} - 3 \times 3 \\ = 27 - 9 \\ = 18$