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電子課本網(wǎng) 第73頁

第73頁

信息發(fā)布者:
解:依題意,可得$a - 199 + b\geq0,$$199 - a - b\geq0,$即$a + b - 199\geq0,$$199-(a + b)\geq0。$故可得$a + b - 199 = 0,$即$a + b = 199$ ①,將其代入原式,可得$\sqrt{3a + 2b - 2 - c}+\sqrt{2a + 3b - c}=0,$則有$\begin{cases}3a + 2b - 2 - c = 0&②\\2a + 3b - c = 0&③\end{cases},$由②+③,得$5(a + b)-2 - 2c = 0$ ④,將①代入④,得$5\times199 - 2 - 2c = 0,$解得$c=\frac{993}{2}。$
B
6
解:由題意得$\sqrt{2y + z}+|x - y|+(z-\frac{1}{2})^2 = 0,$$\therefore 2y + z = 0,$$x - y = 0,$$z-\frac{1}{2}=0,$解得$x=-\frac{1}{4},$$y=-\frac{1}{4},$$z=\frac{1}{2},$則$2x - y + z = 2\times(-\frac{1}{4})-(-\frac{1}{4})+\frac{1}{2}=\frac{1}{4},$$\therefore 2x - y + z$的算術(shù)平方根為$\frac{1}{2}。$
解:
(1)$\because(ab - 2)^2\geq0,$$\sqrt{b - 1}\geq0,$$(ab - 2)^2+\sqrt{b - 1}=0,$$\therefore ab - 2 = 0,$$b - 1 = 0,$$\therefore a = 2,$$b = 1。$
(2)當(dāng)$a = 2,$$b = 1$時(shí),原式$=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\cdots+\frac{1}{2025\times2026}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdots+\frac{1}{2025}-\frac{1}{2026}=1-\frac{1}{2026}=\frac{2025}{2026}。$