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Extraneous solutions of equations
Which value for the constant
c makes
z=2 an extraneous solution in the following equation?

{:[sqrt(7-3z)=3+cz],[c=O/]:}

Extraneous solutions of equations $\newline$ Which value for the constant $c$ makes $z=2$ an extraneous solution in the following equation? $\newline$ $\begin{array}{l} \sqrt{7-3 z}=3+c z \\ c=\emptyset \end{array}$

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Find derivatives of sine and cosine functions

Full solution

Q. Extraneous solutions of equations

\newline

Which value for the constant

c

makes

z=2

an extraneous solution in the following equation?

\newline

\begin{array}{l} \sqrt{7-3 z}=3+c z \\ c=\emptyset \end{array}

Check for Extraneous Solution: Substitute $z=2$ into the equation to check if it's an extraneous solution. $\newline$ $\sqrt{7-3\times 2} = 3 + c\times 2$ $\newline$ $\sqrt{1} = 3 + 2c$ $\newline$ $1 = 3 + 2c$
Solve for c: Solve for c. $\newline$ $1 = 3 + 2c$ $\newline$ $1 - 3 = 2c$ $\newline$ $-2 = 2c$ $\newline$ $c = -1$
Verify Solution: Verify if $z=2$ is indeed an extraneous solution by substituting $c=-1$ back into the original equation. $\newline$ $\sqrt{7-3\cdot 2} = 3 + (-1)\cdot 2$ $\newline$ $1 = 3 - 2$ $\newline$ $1 = 1$

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