Question

Solve for x in the equation x⁶+8=0.

Answer 1

When we solve for x in the given equation, x⁶ + 8 = 0, the result obtained is
`-√(2)`

How to solve for x in the equation given?

The equation given from the question is:

• Equation given: x⁶ + 8 = 0
• Solve for x =?

We can solve for x in the equation, x⁶ + 8 = 0 as illustrated below:

x⁶ + 8 = 0

Subtract 8 from both sides, we have

x⁶ + 8 - 8 = 0 - 8

x⁶ = -8

Recall

8 = 2³

Thus, we have

x⁶ = -2³

Take the sixth root of both x⁶ and -2³

`\sqrt[6]{x^6} = -\sqrt[6]{2^3} \\\\x = -2^{(3)/(6)} \\\\x = -2^{(1)/(2)}\\\\x = -√(2)`

Thus, the solution for x in the equation is
`-√(2)`