Question

Solve and check es001-1.jpg

The solution is c =

How many extraneous solutions are there?

Answer 1

I can’t see the image es001-1.jpg. Please either upload the image here or paste the equation/text from it.

While I wait, here is the exact procedure I will use once I can see the problem (so you know what I’ll check):

1. Identify domain restrictions (values that make denominators zero, or make even-indexed radicands negative, etc.). Exclude those before solving.
2. Solve the equation algebraically (clear denominators, isolate radicals and square if necessary, etc.).
3. Each time you perform a non-reversible operation (multiplying by an expression that might be zero, squaring both sides, etc.) note that new candidate solutions might be introduced.
4. Substitute each candidate solution back into the original equation to see whether it satisfies the equation.
5. The solutions that satisfy are the true solutions; any candidates that do not satisfy the original equation are extraneous. Count them.

If you upload or paste the equation, I will solve it step by step, give the final value(s) of c, and tell you how many extraneous solutions there are.