HOC24
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Bài 1:
Gọi số tự nhiên cần tìm là a.
Theo bài ra ta có: \(\left\{{}\begin{matrix}4a⋮26\\5a⋮11\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a⋮13\left(vì\left(4,26\right)=2\right)\\a⋮11\left(vì\left(5,11\right)=1\right)\end{matrix}\right.\)
Vì a là số tự nhiên nhỏ nhất nên a=[13,11]=143
vậy số cần tìm là 143
phần đầu đúng ko?
* Ta đi CM tổng quát: \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\) (1)
Có: \(\left\{{}\begin{matrix}\left|a\right|\ge a;\left|a\right|\ge-a\\\left|b\right|\ge b;\left|b\right|\ge-b\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left|a\right|+\left|b\right|\ge a+b\\\left|a\right|+\left|b\right|\ge-\left(a+b\right)\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left|a\right|+\left|b\right|\ge a+b\\-\left(\left|a\right|+\left|b\right|\right)\le a+b\end{matrix}\right.\)
\(\Rightarrow-\left(\left|a\right|+\left|b\right|\right)\le a+b\le\left|a\right|+\left|b\right|\)
\(\Rightarrow\left|a\right|+\left|b\right|\ge\left|a+b\right|\left(ĐPCM\right)\)
Có: \(\left|x\right|+\left|x-2\right|=\left|x\right|+\left|2-x\right|\) (2)
Áp dụng t/c (1) vào (2), ta đc: \(\left|x\right|+\left|2-x\right|\ge\left|x+2-x\right|=\left|2\right|=2\)
b) tg tự như phần a
a) \(\left|1-3x\right|-x-2=0\)
\(\Rightarrow\left|1-3x\right|=x+2\)
Có: \(\left|1-3x\right|=\left\{{}\begin{matrix}1-3x\forall x\le\dfrac{1}{3}\\3x-1\forall x>\dfrac{1}{3}\end{matrix}\right.\)
Xét: \(x\le\dfrac{1}{3}.\) Khi đó: 1 - 3x = x+2
\(\Rightarrow x=-\dfrac{1}{4}\)
Xét: \(x>\dfrac{1}{3}\) Khi đó: 3x - 1 = x + 2
\(\Rightarrow x=\dfrac{3}{2}\)
vậy \(x=-\dfrac{1}{4}orx=\dfrac{3}{2}\)
a) Có: \(\left\{{}\begin{matrix}\left|x+1\right|\ge0\\\left|x+2\right|\ge0\\\left|x+3\right|\ge0\end{matrix}\right.\Rightarrow4x\ge0\Rightarrow x\ge0\Rightarrow\left\{{}\begin{matrix}x+1\ge0\\x+2\ge0\\x+3\ge0\end{matrix}\right.\)
\(\Rightarrow x+1+x+2+x+3=4x\)
\(\Rightarrow3x+6=4x\)
\(\Rightarrow x=6\)
Có: \(\left|x\right|+\left|x-2\right|=\left|x\right|+\left|2-x\right|\ge\left|x+2-x\right|=2\)
Để \(\left|x\right|+\left|x-2\right|=2\) thì \(x\left(2-x\right)\ge0\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\2-x\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x\le0\\2-x\le0\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\x\le2\end{matrix}\right.\\\left\{{}\begin{matrix}x\le0\\x\ge2\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}0\le x\le2\left(TM\right)\\0\ge x\ge2\left(loai\right)\end{matrix}\right.\)
Vậy \(0\le x\le2\)
We often go to school by bike.
Why should you reduce the use of fossil fuels?
Choose the best answer to complete the sentence:
You can write with ... a ballpoint pen or a pencil.
A. both B. either
C. also D. as well
Tìm x, y là các số hữu tỉ biết:
a) \(x\sqrt{3}+3=y\sqrt{3}-x\)
b) \(\left(x-2\right)\sqrt{25n^2+5}+y-2=0\)