Solve the equation.
-$$\left| x ^ { 2 } + 9 \right| = | 6 x |$$
A) $\{ - 3 \}$
B) $\{ - 3,3 \}$
C) $\varnothing$
D) $\{ 3 \}$

Question

Quizplus · Accepted Answer

The equation $\left| x ^ { 2 } + 9 \right| = | 6 x |$ can be solved by considering the absolute value properties. Since both sides are absolute values, we square both sides to eliminate the absolute values, leading to $x^2 + 9 = 36x$, which simplifies to $x^2 - 36x + 9 = 0$. However, the correct approach is to consider cases due to the absolute values: 1. $x^2 + 9 = 6x$ and 2. $x^2 + 9 = -6x$.Solving these equations directly as they are (without squaring both sides incorrectly) will lead to the realization that the original equation does not have real solutions that satisfy both conditions simultaneously due to the nature of absolute values. However, considering the mistake in the explanation process, the correct approach involves breaking it down into two cases based on the definition of absolute value:1. For $x^2 + 9 = 6x$, we rearrange to get $x^2 - 6x + 9 = 0$, which factors to $(x-3)^2 = 0$, giving $x = 3$.2. For $x^2 + 9 = -6x$, we rearrange to get $x^2 + 6x + 9 = 0$, which factors to $(x+3)^2 = 0$, giving $x = -3$.Therefore, both $x = 3$ and $x = -3$ are solutions, making the correct choice B.

Solve the Equation ∣x2+9∣=∣6x∣\left| x ^ { 2 } + 9 \right| = | 6 x |​x2+9​=∣6x∣

Solve the Equation $\left| x ^ { 2 } + 9 \right| = | 6 x |$