Solve the radical equation, if possible. $$\sqrt { 49 m ^ { 2 } - 4 m + 10 } = 7 m - 8$$
A) $\left\{ \frac { 1 } { 2 } \right\}$
B) $\{ - 2,2 \}$
C) $\left\{ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right\}$
D) \{ \}

Question

Quizplus · Accepted Answer

To solve the radical equation $\sqrt { 49 m ^ { 2 } - 4 m + 10 } = 7 m - 8$, we first square both sides to eliminate the square root, resulting in $49m^2 - 4m + 10 = 49m^2 - 112m + 64$. Simplifying this equation by subtracting $49m^2$ from both sides and rearranging terms gives $108m = 54$, or $m = \frac{1}{2}$. However, when we substitute $m = \frac{1}{2}$ back into the original equation to check for extraneous solutions, we find that the left side becomes $\sqrt{49(\frac{1}{2})^2 - 4(\frac{1}{2}) + 10}$ which does not equal the right side $7(\frac{1}{2}) - 8$. Therefore, $m = \frac{1}{2}$ is not a solution, and the correct answer is that there are no solutions, represented by the empty set $\{\}$.

Solve the Radical Equation, If Possible 49m2−4m+10=7m−8\sqrt { 49 m ^ { 2 } - 4 m + 10 } = 7 m - 849m2−4m+10​=7m−8

Solve the Radical Equation, If Possible $\sqrt { 49 m ^ { 2 } - 4 m + 10 } = 7 m - 8$