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

Aug 12, 2016

$x = 3$

#### 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.

${\sqrt[4]{6 x - 5}}^{4} = {\sqrt[4]{x + 10}}^{4}$

$6 x - 5 = x + 10$

$5 x = 15$

$x = 3$

Aug 12, 2016

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

${\left(\sqrt[4]{6 x - 5}\right)}^{4} = {\left(\sqrt[4]{x + 10}\right)}^{4}$

$6 x - 5 = x + 10$

$5 x = 15$

$x = 3$

Checking in the original equation, we have that:

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

$\sqrt[4]{13} = \sqrt[4]{13}$

Hence, the solution is correct; the solution set to this equation is $\left\{3\right\}$.

Hopefully this helps!