a, 25/12

b,  25/72

a) = 3/4 + 4/3 = 25/12

b) = 3/8 - 16/9 = -101/72 * hình như hơi sai sai:"> *

\(5.a.V_{rượu}=\dfrac{46.25}{100}=11,5\left(l\right)\\ m_{rượu}=11,5.0,8=9,2\left(g\right)\\ b.C_2H_5OH+CH_3COOH⇌CH_3COOC_2H_5+H_2O\\n_{C_2H_5OH}=\dfrac{9,2}{46}=0,2\left(mol\right)\\ n_{CH_3COOC_2H_5}=n_{C_2H_5OH}=0,2\left(mol\right)\\ \Rightarrow m_{CH_3COOC_2H_5}=0,2.88=17,6\left(g\right)\\ VìH=30\%\Rightarrow m_{CH_3COOC_2H_5}=17,6.30\%=5,28\left(g\right)\)

\(6.a.C_2H_5OH+CH_3COOH⇌CH_3COOC_2H_5+H_2O\\ n_{C_2H_5OH}=\dfrac{23}{46}=0,5\left(mol\right)\\ n_{CH_3COOH}=0,5.60=30\left(g\right)\\ b.n_{CH_3COOC_2H_5}=n_{C_2H_5OH}=0,5\left(mol\right)\\ \Rightarrow m_{CH_3COOC_2H_5}=0,5.88=44\left(g\right)\\ VìH=70\%\Rightarrow m_{CH_3COOC_2H_5}=44.70\%=30,8\left(g\right)\)

=(-1+2)-(3+4)-(5+6)-........-(2017+2018)

=1-7-11-........-4035

=-1009

\(b,N=\left(2x-1\right)^2-4\ge-4\\ N_{min}=-4\Leftrightarrow x=\dfrac{1}{2}\\ c,P=\left(2x-5\right)^2+6\left(2x-5\right)+9-4\\ P=\left(2x-5+3\right)^2-4=\left(2x-2\right)^2-4\ge-4\\ P_{min}=-4\Leftrightarrow x=1\\ d,Q=\left(x^2-2x+1\right)+\left(y^2+4y+4\right)+1\\ Q=\left(x-1\right)^2+\left(y+2\right)^2+1\ge1\\ Q_{min}=1\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-2\end{matrix}\right.\)

6a.

$M=x^2-x+1=(x^2-x+\frac{1}{4})+\frac{3}{4}$

$=(x-\frac{1}{2})^2+\frac{3}{4}\geq \frac{3}{4}$

Vậy $M_{\min}=\frac{3}{4}$ khi $x-\frac{1}{2}=0\Leftrightarrow x=\frac{1}{2}$

ĐKXĐ: \(-2\le x\le3\)

\(\dfrac{\sqrt{-x^2+x+6}}{2x+5}-\dfrac{\sqrt{-x^2+x+6}}{x-4}\ge0\)

\(\Leftrightarrow\sqrt{-x^2+x+6}\left(\dfrac{1}{2x+5}-\dfrac{1}{x-4}\right)\ge0\)

\(\Leftrightarrow\dfrac{\left(-x-9\right)\sqrt{x^2+x+6}}{\left(2x+5\right)\left(x-4\right)}\ge0\)

\(\Leftrightarrow\left[{}\begin{matrix}-x^2+x+6=0\\\dfrac{-x-9}{\left(2x+5\right)\left(x-4\right)}\ge0\end{matrix}\right.\) \(\Leftrightarrow-2\le x\le3\)

Hoặc có thể biện luận như sau:

Ta có: \(\left\{{}\begin{matrix}2x+5>0;\forall x\in\left[-2;3\right]\\x-4< 0;\forall x\in\left[-2;3\right]\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{\sqrt{-x^2+x+6}}{2x+5}\ge0\\\dfrac{\sqrt{-x^2+x+6}}{x-4}\le0\end{matrix}\right.\) ; \(\forall x\in\left[-2;3\right]\)

Do đó nghiệm của BPT là \(-2\le x\le3\)

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