Question

下列哪个方程没有解？

Which of the following equations does not have a solution?

$(x + 7)^2 = 0$

$|-3x| + 5 = 0$

$\sqrt{-x} - 2 = 0$

$\sqrt{x} - 8 = 0$

$|-3x| - 4 = 0$

找出哪个方程要求一个非负表达式等于负数。

Check which equation asks a nonnegative expression to be negative

绝对值加 $5$ 不可能等于 $0$ 。

An absolute value plus $5$ cannot equal $0$

选项 A 化为 $x + 7 = 0$ $x = -7\text{，}$ 因此有解。

选项 B 化为 $|-3x| = -5\text{，}$ 绝对值不可能为负数，因此无解。

其他选项都有解，如下面计算所示。

选项 C 化为 $\sqrt{-x} = 2$ $-x = 4$ $x = -4\text{，}$ 所以有解。

选项 D 化为 $\sqrt{x} = 8$ $x = 64\text{，}$ 所以也有解。

最后，选项 E 化为 $|-3x| = 4$ $-3x = \pm 4$ $x = \pm \dfrac{4}{3}\text{，}$ 同样有解。

所以正确答案是 B。

A simplifies to $x + 7 = 0$ $x = -7,$ so it has a solution.

B simplifies to $|-3x| = -5,$ which has no solution since absolute value makes everything positive.

Let us make sure that all the other choices have solutions.

C simplifies to $\sqrt{-x} = 2$ $-x = 4$ $x = -4,$ which is fine.

D simplifies to $\sqrt{x} = 8$ $x = 64,$ which works.

Finally, E simplifies to $|-3x| = 4$ $-3x = \pm 4$ $x = \pm \dfrac{4}{3},$ which has a solution as well.

Thus, B is the correct answer.