Which value for the constant c makes w=5 an extraneous solution in the following equation? {:[sqrt(29+4w)=23-cw],[c=]:}

Question

Which value for the constant  c makes  w=5 an extraneous solution in the following equation?  {:[sqrt(29+4w)=23-cw],[c=]:}

Bytelearn · Accepted Answer

Understand Extraneous Solution: Understand what an extraneous solution is. An extraneous solution is a solution that emerges from the process of solving an equation but is not a valid solution to the original equation. In this case, we want to find a value for c that makes w=5 an extraneous solution for the given equation.Substitute and Simplify: Substitute w=5 into the equation and simplify. We substitute w=5 into the left side of the equation sqrt(29+4w) to see what happens. sqrt(29+4(5)) = sqrt(29+20) = sqrt(49) = 7Set Equal and Solve: Substitute w=5 into the right side of the equation and simplify. Now we substitute w=5 into the right side of the equation 23-cw to find the value of c that would make w=5 an extraneous solution. 23-c(5) = 23-5cSolve for c: Set the two sides of the equation equal to each other. Since we want w=5 to be an extraneous solution, the two sides of the equation should not be equal when w=5. However, to find the value of c that would make this happen, we first set the two sides equal to each other and solve for c. 7 = 23-5cVerify Extraneous Solution: Solve for c. Now we solve the equation for c. 5c = 23-7 5c = 16 c = 16/5 c = 3.2Verify that w=5 is an extraneous solution for the found value of c. We need to check that for c=3.2, the original equation does not hold true when w=5. This means that the two sides of the equation should not be equal when w=5. Left side: sqrt(29+4(5)) = sqrt(49) = 7 Right side: 23-3.2(5) = 23-16 = 7 Since both sides are equal, w=5 is not an extraneous solution for c=3.2. This means we made a mistake in our assumption that setting the two sides equal would give us the extraneous solution.

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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Which value for the constant c c c makes w=5 w=5 w=5 an extraneous solution in the following equation?\newline29+4w=23−cwc=□ \begin{array}{l} \sqrt{29+4 w}=23-c w \\ c=\square \end{array} 29+4w​=23−cwc=□​

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