Question

If x-1/x=4 then evaluate x^2-1/x^2 and x^4-1/x^4

Answer 1

$\huge{\underline{\underline{\green{\mathfrak{Answer:}}}}}$

Given: $\large\mathbf{\frac{x - 1}{x} = 4}$

let us find the value of x

=> $\mathbf{x - 1 = 4x}$

=> $\mathbf{3x = -1}$

=> $\mathbf{x = \frac{- 1}{3}}$

Now, putting values of x

=> $\large\mathbf{\frac{x^2 - 1}{x^2} = \frac{(\frac{-1}{3})^2 - 1}{(\frac{-1}{3})^2}}$

=> $\large\mathbf{\frac{\frac{1}{9} - 1}{\frac{1}{9}}}$

=> $\large\mathbf{\frac{-8}{9} × \frac{9}{1}}$

=> $\large\fbox{\mathbf{-8}}$

And,

=> $\large\mathbf{\frac{x^4 - 1}{x^4} = \frac{(\frac{-1}{3})^4 - 1}{(\frac{-1}{3})^4}}$

=> $\large\mathbf{\frac{\frac{1}{81} - 1}{\frac{1}{81}}}$

=> $\large\mathbf{\frac{-80}{81} × \frac{81}{1}}$

=> $\large\fbox{\mathbf{-80}}$