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

Question

07-04-2021
Mathematics

Answered

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

Sagot :

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Sqdancefanidn Sqdancefanidn · Answer 1 · 2021-04-07T15:16:34-04:00

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Answer:

True

Step-by-step explanation:

We assume your equation is intended to be ...

[tex]\sqrt{x+56} =x[/tex]

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

[tex]x+56=x^2\\\\x^2-x-56=0\\\\(x-8)(x+7)=0\longrightarrow x=\{-7,+8\}[/tex]

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.

Sagot :

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