Question

A number x is twice its reciprocal. What is x^6?

Answer 1

Answer:

8

Step-by-step explanation:

x = 2/x <=== It must be: x ≠ 0. Solve for x. Multiply both sides by x.

x^2 = 2.

Hence:

x = ±√2.

Both -√2 and √2 give 8 when they are raised to the power of 6.

(-√2)^6 = (√2)^6 = 8.

Answer 2

The value of the given expression $x^6$ is 8 and this can be determined by using the arithmetic operations.

Given :

A number x is twice its reciprocal.

The following steps can be used in order to determine the value of $x^6$:

Step 1 - The arithmetic operations can be used in order to determine the value of $x^6$.

Step 2 - The mathematical expression of the given statement "A number x is twice its reciprocal" is:

$x = \dfrac{2}{x}$

Step 3 - Simplify the above expression in order to determine the value of 'x'.

$x = \pm\sqrt{2}$

Step 4 - Now, substitute the value of 'x' in the given expression.

$x^6= (\sqrt{2} )^6\\x^6 = 8$

So, the value of the given expression $x^6$ is 8.

For more information, refer to the link given below:

https://brainly.com/question/25834626