Question

if x⁴+1/x⁴=4 then x-1/x is equal to​

Answer 1

Step-by-step explanation:

Let

$x - \frac{1}{x} = k$

Squaring On Both Sides

${x}^{2} + \frac{1}{ {x}^{2} } = {k}^{2} + 2$

Squaring On Both Sides

${x}^{4} + \frac{1}{ {x}^{4} } = {k}^{4} + 2 {k}^{2} + 2$

Given,

${x}^{4} + \frac{1}{ {x}^{4} } = 4$

Let k² = t

Then,

$4 = {t}^{2} + 2t + 2$

On solving this, you get t value. From that you get k value.

Please mark as brainliest and follow

Answer 2

Step-by-step explanation:

$\frac{ {x}^4({1 + \frac{1}{ {x}^4{} } )} }{ {x}^4{} } = 4 \\ 1 + \frac{1}{ {x}^4{} } = 4 \\ \frac{1}{ {x}^4{} } = 3 \\ x = \frac{1}{ { \sqrt[4]{3} }{} } \\</p><p>[tex]x - \frac{1}{x } = \frac{1}{ \sqrt[4]{3} } - \sqrt[4]{3} = \frac{1 - ( \sqrt[]{3} )}{ \sqrt[4]{3} }$