Question

Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate. 5x^6=30

Answer 1

The real solutions are

`x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35`

Explanation:

The solution, or root, of an equation is any value or set of values that can be substituted into the equation to make it a true statement.

To find the real solutions of the equation
`5x^6=30`:

`\mathrm{Divide\:both\:sides\:by\:}5\\\\(5x^6)/(5)=(30)/(5)\\\\\mathrm{Simplify}\\\\x^6=6\\\\\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)}\\\\x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35`