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$Woo Jin is solving the following equation for x. 7-4x=sqrt(x+3) His first few steps are given below. {:[(7-4x)^(2)=(sqrt(x+3))^(2)],[49-56 x+16x^(2)=x+3]:} Is it necessary for Woo Jin to check his answers for extraneous solutions? Choose 1 answer: (A) Yes (B) No$

Woo Jin is solving the following equation for $x$ . $\newline$ $7-4 x=\sqrt{x+3}$ $\newline$ His first few steps are given below. $\newline$ $\begin{aligned} (7-4 x)^{2} & =(\sqrt{x+3})^{2} \\ 49-56 x+16 x^{2} & =x+3 \end{aligned}$ $\newline$ Is it necessary for Woo Jin to check his answers for extraneous solutions? $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) $\mathrm{No}$

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Counting principle

Full solution

Q. Woo Jin is solving the following equation for

x

.

\newline

7-4 x=\sqrt{x+3}

\newline

His first few steps are given below.

\newline

\begin{aligned} (7-4 x)^{2} & =(\sqrt{x+3})^{2} \\ 49-56 x+16 x^{2} & =x+3 \end{aligned}

\newline

Is it necessary for Woo Jin to check his answers for extraneous solutions?

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B)

\mathrm{No}

Identify Extraneous Solutions: Woo Jin is solving an equation that involves a square root. When both sides of an equation are squared, as Woo Jin has done, there is a possibility that extraneous solutions may be introduced. These are solutions that fit the squared form of the equation but do not satisfy the original equation. Therefore, it is necessary to check for extraneous solutions.

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