Question

The equation (x+56)1/2^=x has an extraneous solution. True or false

Answer 1

9514 1404 393

Answer:

  True

Step-by-step explanation:

We assume your equation is intended to be ...

  $\sqrt{x+56} =x$

The usual method of solution squares both sides, then solves the resulting quadratic.

  $x+56=x^2\\\\x^2-x-56=0\\\\(x-8)(x+7)=0\longrightarrow x=\{-7,+8\}$

Considering the initial problem, we require x ≥ 0, so the x=-7 solution is extraneous.

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A graphical solution shows there is only one value of x that satisfies the equation. The other "solution" arises from considering the negative square root. It is introduced when the equation is squared.