Math CentralQuandaries & Queries


Question from Eileen, a student:

Checking for extraneous solutions


Hi Eileen,

I would rewrite the equation as

\[(5x + 4)^{1/2} = 3x\]

and then square both sides. This will result in a quadratic which you can factor to obtain two solutions. These are solutions to the quadratic but not necessarily solutions to $(5x + 4)^{1/2} = 3x.$ To check whether they are solutions to $(5x + 4)^{1/2} = 3x$ you need to substitute them into the equation and see if the equation is satisfied. I can see two ways a solution to the quadratic might not satisfy the original equation. First $5x + 4$ might be negative so that you can't take its square root or secondly $3x$ might be negative although the left side can't be negative,

I hope this helps,

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