Solution assignment 07 Root equations

Solve:

Solution

We can first try to write the conditions which must be met for which this equation is defined. We can also begin solving the equation and check afterwards whether solutions satisfy the equation. We now choose the second approach.
We square both sides of the equation:

We can solve this quadratic equation by factorization:

and thus:

or

Now we check whether these solutions satisfy the original equation. The second solution satisfies the equation, but the first one does not:

but:

Thus the solution of the original equation is: