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Extraneous solutions of equations
Which value for the constant
c makes
w=5 an extraneous solution in the following equation?

{:[sqrt(29+4w)=23-cw],[c=◻]:}

Extraneous solutions of equations $\newline$ Which value for the constant $c$ makes $w=5$ an extraneous solution in the following equation? $\newline$ $\begin{array}{l} \sqrt{29+4 w}=23-c w \\ c=\square \end{array}$

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Find derivatives of logarithmic functions

Full solution

Q. Extraneous solutions of equations

\newline

Which value for the constant

c

makes

w=5

an extraneous solution in the following equation?

\newline

\begin{array}{l} \sqrt{29+4 w}=23-c w \\ c=\square \end{array}

Substitute $w=5$ : Step $1$ : Substitute $w=5$ into the equation. $\sqrt{29 + 4\times 5} = 23 - c\times 5$
Simplify left side: Step $2$ : Simplify the left side of the equation. $\sqrt{49} = 23 - 5c$
Evaluate $\sqrt{49}$ : Step $3$ : Evaluate $\sqrt{49}$ . $7 = 23 - 5c$
Solve for c: Step $4$ : Solve for c. $\newline$ $7 = 23 - 5c$ $\newline$ $5c = 23 - 7$ $\newline$ $5c = 16$ $\newline$ $c = \frac{16}{5}$ $\newline$ $c = 3.2$
Check extraneous solution: Step $5$ : Check if $w=5$ is an extraneous solution. $\newline$ Substitute $w=5$ and $c=3.2$ back into the original equation. $\newline$ $\sqrt{29 + 4\times 5} = 23 - 3.2\times 5$ $\newline$ $\sqrt{49} = 23 - 16$ $\newline$ $7 = 7$ $\newline$ Since both sides are equal, $w=5$ is not extraneous for $c=3.2$ .

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