Tìm x:
\(2^1_2x+x=2^2_{15}\)
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\(\left|\dfrac{1}{2}x+3\right|=\dfrac{2}{5}\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x+3=\dfrac{2}{5}\\\dfrac{1}{2}x+3=-\dfrac{2}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x=-\dfrac{13}{5}\\\dfrac{1}{2}x=-\dfrac{17}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{26}{5}\\x=-\dfrac{34}{5}\end{matrix}\right.\\ \Rightarrow S=\left\{-\dfrac{26}{5};-\dfrac{34}{5}\right\}\)
`|1/2x+3|=2/5`
`+)1/2x+3=2/5`
`<=>1/2x=-13/5`
`<=>x=-26/5`
`+)1/2x+3=-2/5`
`<=>1/2x=-17/5`
`<=>x=-34/5`
Vậy `x=-26/5` hoặc `x=-34/5`
Để \(\left(x^2-2\right)\left(x^2-10\right)\le0\)
=> Có 2 trường hợp , ta có :
\(\left(1\right)\hept{\begin{cases}x^2-2\le0\\x^2-10\ge0\end{cases}\Rightarrow\hept{\begin{cases}x^2\le2\\x^2\ge10\end{cases}}\Rightarrow x\in O}\)
\(\left(2\right)\hept{\begin{cases}x^2-2\ge0\\x^2-10\le0\end{cases}\Rightarrow\hept{\begin{cases}x^2\ge2\\x^2\le10\end{cases}\Rightarrow2\le x^2\le}10}\)
=> x = {2 ; 3}
b) Để \(\frac{2}{3\left|x-1\right|+4}\)đạt GTLN
=> 3|x - 1|+ 4 đạt giá trị nhỏ nhất
mà 3|x - 1| \(\ge0\forall x\)
=> 3|x - 1| + 4 \(\ge\)4
Dấu "=" xảy ra <=> x - 1 = 0
=> x = 1
Vậy GTLN của \(B=\frac{1}{2}\Leftrightarrow x=1\)
ĐK: \(x\ge4\)
\(\dfrac{\left(x-2\right)!}{\left(x-4\right)!}+\dfrac{x!}{\left(x-2\right)!.2!}=101\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)+\dfrac{x\left(x-1\right)}{2}=101\)
\(\Leftrightarrow3x^2-11x-190=0\)
\(\Rightarrow x=10\)
a)\(\left(x-140\right)\)\(\div\)7=27-4-3 =20\(\Rightarrow\) \(\left(x-140\right)\) =20x7=140\(\Rightarrow\) x=0
2\(\frac{1}{2}\)x+x=2\(\frac{2}{15}\)\(\Rightarrow\)\(\frac{5}{2}\)x+x=\(\frac{32}{15}\)\(\Rightarrow\)x(\(\frac{5}{2}\)+1)=\(\frac{32}{15}\)\(\Rightarrow\)x.\(\frac{7}{2}\)=\(\frac{32}{15}\)\(\Rightarrow\)x=\(\frac{32}{15}\):\(\frac{7}{2}\)\(\Rightarrow\)x=\(\frac{32}{15}\).\(\frac{2}{7}\)\(\Rightarrow\)x=\(\frac{64}{105}\)
Giải
\(2\frac{1}{2}x-x=2\frac{2}{15}=>\frac{5}{2}x-x=\frac{32}{15}=>x\left(\frac{5}{2}-1\right)=\frac{32}{15}=>x.\frac{7}{2}=\frac{32}{15}=>x=\frac{32}{15}:\frac{7}{2}=>x=\frac{64}{105}\)