AMC10 2011 A

AMC10 2011 A · Q7

AMC10 2011 A · Q7. It mainly tests Absolute value, Exponents & radicals.

Which of the following equations does not have a solution?

下列哪个方程没有解？

(A) $(x + 7)^2 = 0$ $(x + 7)^2 = 0$

(B) $| -3x| + 5 = 0$ $| -3x| + 5 = 0$

(D) $\sqrt{x -8} = 0$ $\sqrt{x -8} = 0$

(E) $| -3x| -4 = 0$ $| -3x| -4 = 0$

Answer

Correct choice: (B)

正确答案：（B）

Solution

Because $|−3x|+5$ is strictly positive, the equation $|−3x|+5 = 0$ has no solution. The solutions of equations (A), (C), (D), and (E) are −7, −4, 64, and $\pm \frac{4}{3}$, respectively.

因为$|−3x|+5$严格大于0，方程$|−3x|+5 = 0$没有解。方程(A)、(C)、(D)和(E)的解分别是$-7$、$-4/3$、64和$\pm \frac{4}{3}$。

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