When solving radical equations if the check results in an imaginary number is the solution extraneous?

Question

(-4x+17)^1/2 = (28-5x)^1/2

x=11

Check: (-27)^1/2 = (-27)^1/2

Since the square root of -27 is imaginary is the solution extraneous even though both sides equal each other?

Answer 1

Hello Heather,

That is correct. You said it all. If you take the square root of a negative number, the answer is not real but imaginary. Therefore, x = 11 would be extraneous and this equation would have no solution.