1. Tìm x:
a) 1,5 - 2 . /x/ = -0,5
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a) \(1=\left(2x+0,5\right)^{600}\)
\(\Rightarrow1^{600}=\left(2x+0,5\right)^{600}\)
\(\Rightarrow\left[{}\begin{matrix}2x+0,5=1\\2x+0,5=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=0,5\\2x=-1,5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0,25\\x=-0,75\end{matrix}\right.\)
b) \(\left(x-0,125\right)^2=0,25\)
\(\Rightarrow\left(x-0,125\right)^2=0,5^2\)
\(\Rightarrow\left[{}\begin{matrix}x-0,125=0,5\\x-0,125=-0,5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0,625\\x=-0,375\end{matrix}\right.\)
c) \(\left(x-3\right)^{11}=\left(x-3\right)^{41}\)
\(\Rightarrow\left(x-3\right)^{11}-\left(x-3\right)^{41}=0\)
\(\Rightarrow\left(x-3\right)^{11}\left[1-\left(x-3\right)^{30}\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-3\right)^{11}=0\\\left(x-3\right)^{30}=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x-3=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
`@` `\text {Ans}`
`\downarrow`
`a)`
`1 = (2x + 0,5)^600`
`=> (2x+0,5)^600 = (+-1)^600`
`=> \text {TH1: } 2x + 0,5 = 1`
`=> 2x = 1 - 0,5`
`=> 2x = 0,5`
`=> x = 0,5 \div 2`
`=> x = 0,25`
`\text {TH2: } 2x + 0,5 = -1`
`=> 2x = -1 - 0,5`
`=> 2x = -1,5`
`=> x = -1,5 \div 2`
`=> x = -0,75`
Vậy, `x \in {-0,75; 0,25}.`
`b)`
`(x - 0,125)^2 = 0,25`
`=> (x - 0,125)^2 = (+-0,5)^2`
`=> `\(\left[{}\begin{matrix}x-0,125=0,5\\x-0,125=-0,5\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=0,5+0,125\\x=-0,5+0,125\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=0,625\\x=-0,375\end{matrix}\right.\)
Vậy, `x \in {-0,375; 0,625}.`
`c)`
`(x - 3)^11 = (x - 3)^41`
`=> (x - 3)^11 - (x - 3)^41 = 0`
`=> (x - 3)^11 * [ 1 - (x - 3)^30] = 0`
`=>`\(\left[{}\begin{matrix}\left(x-3\right)^{11}=0\\1-\left(x-3\right)^{30}=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x-3=0\\\left(x-3\right)^{30}=1\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=3\\x-3=1\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
Vậy, `x \in {3; 4}.`
a: x=2/3-4/5=10/15-12/15=-2/15
b: 1/2-x=7/12
=>x=1/2-7/12=-1/12
c: =>7/2:x=-7/2
=>x=-1
d: =>1/6x=3/8-5/2=3/8-20/8=-17/8
=>x=-17/8*6=-102/8=-51/4
e: =>1,5x=-1,5
=>x=-1
1)\(x+0,5+x+1,5+x+2,5=33\)
\(\Leftrightarrow3x=33-0,5-1,5-2,5=28,5\)
\(\Leftrightarrow x=9,5\)
2)\(\left(x+0,9\right)\left(1-0,4\right)=2412\)
\(\Leftrightarrow\left(x+0,9\right)\cdot0,6=2412\)
\(\Leftrightarrow x+0,9=4020\)
\(\Leftrightarrow x=1019,1\)
4028 x 0,5 + 4028 + 2014 : \(\dfrac{1}{2}\) x 1,5 + 4028 : 0,5
= 4028 x 0,5 + 4028 x 1 + 2014 x 2 x 1,5 + 4028 x 2
= 4028 x 0,5 + 4028 x 1 + 4028 x 1,5 + 4028 x 2
= 4028 x ( 0,5 + 1 + 1,5 + 2)
= 4028 x 5
= 20140
Lời giải:
$x+\frac{2}{-15}=\frac{-5}{3}$
$x=\frac{-5}{3}-\frac{2}{-15}=\frac{-5}{3}+\frac{2}{15}$
$x=\frac{-23}{15}$
a)\(1,5-2\left|x\right|=-0,5\)
\(\Leftrightarrow2\left|x\right|=1,5+0,5\)
\(\Leftrightarrow\left|x\right|=1\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)