How do you solve #sqrt(x+4) +sqrt(2x-1)=3sqrt(x-1)#?
Before solving, let's determine the restrictions on the variable. A radical is undefined it the number inside is less than 0.
We must therefore set up an inequality and solve:
Solving each we get that
We must pick the largest of these, since if we pick one of the smaller ones the equation will become undefined. The largest is
In this case, two radicals are undefined. Now that we have defined any restrictions on the variable, we can proceed with solving. This can be started by squaring both sides
Since the radicals are both square roots, we can combine them in multiplication.
Checking both answers in the original equation, we find that only
Therefore, our solution set is
Hopefully this helps!