Question

How do you solve `root4(6x-5)=root4(x+10)`?

Answer 1

`x=3`

Explanation:

Raise the whole equation to the power of 4.
There is only term on each side, so this is quite easy to do and we will get rid of the radicals in this way.

`root4(6x-5)^4=root4(x+10)^4`

`6x - 5 = x + 10`

`5x = 15`

`x = 3`

Answer 2

Put both sides to the 4th power and solve the resulting linear equation.

`(root(4)(6x - 5))^4 = (root(4)(x + 10))^4`

`6x - 5 = x + 10`

`5x = 15`

`x = 3`

Checking in the original equation, we have that:

`root(4)(6 xx 3 - 5) =^? root(4)(3 + 10)`

`root(4)(13) = root(4)(13)`

Hence, the solution is correct; the solution set to this equation is `{3}`.

Hopefully this helps!