Question

If x-1/x = 119. Find the value of x^3-1/x^3

Answer 1

Answer:

69.005

Step-by-step explanation:

Questions

$x - \frac{1}{x} = 119.find \: the \: value \: of \: {x}^{3} - \frac{1}{ {x}^{3} }$

Formula used

${(x - \frac{1}{x}) }^{2} = {x}^{2} + ({ \frac{1}{x} })^{2} + 2 \\ {(x + \frac{1}{x} )}^{2} - {(x - \frac{1}{x}) }^{2} = 4$

Solutions

X - 1/X = 119

On squaring both side

(X - 1/X)^2 = 14161

x^2 + 1/x^2 = 14163 (from above formula )

Now

Since

(X + 1/X)^2 = X^2 + 1/X^2 +2

(X + 1/X)^2 = 14163 + 2

X + 1/X = √( 14165)

X + 1/X = 119.01(equation 2)

on adding equation 1 and 2 we get

2x = 138.01

X = 138.01/2

X= 69.005