Question

I started to solve a radical equation in this way...but both solutions are extraneous because they don't satisfy the original equation...what error did I make?

Answer 1

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Answer 2

You can't do something like \(\huge \sqrt{-2x+1}=x+3\) \(\huge \sqrt{-2x+1-1}=x+3-1\)
\(\huge \sqrt{-2x}=x+2\)

Answer 3

square both sides to cancel the root

Answer 4

So my mistake was subtracting the ones before squaring the root?

Answer 5

Thank you.

Answer 6

correct, you'd have to do something like
\(\huge \sqrt{-2x+1}^2={(x+3)}^2\)

Answer 7

Oh, okay. Thanks! You're much help! ;D