Question

if
$x - \frac{1}{x} = 2$
then find.
${x}^{4} - \frac{1}{ {x}^{2} }$

Answer 1

Answer:

Step-by-step explanation:

Hello there,

Given (x - (1/x)) = 2

Multiplying x on both sides.

=> x² - 1 = 2x

=> x² - 2x - 1 = 0

Here a = 1, b = -2, c = -1

By using the quadratic formula,

We get x = 1 +- √2

By binomial expansion,

x^4 = (1+-√2)^4 = 17 +- 12√2 -----------(1)

1/(x²) = 1/(1+-√2)² = 3-+√2 ---------(2)

Subtracting (2) from (1):

We get (x^4) - (1/x²) = 14(1+-√2)

Hence the answer is 14(1+-√2).

Hope my answer helps you.

Harith