Tìm x, biết:
b) 30 % x - x + 5 6 = 1 3
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\(35-5\left(x-1\right)=10\\ \Leftrightarrow35-5x+5=10\\ \Rightarrow40-5x=10\)
\(\Rightarrow-5x=10-40\\ \Rightarrow-5x=-30\\ \Rightarrow x=\dfrac{-30}{-5}=6\)
c)
\(24\left(x-16\right)=12^2\)
\(\Rightarrow24x-384=144\\ \Rightarrow24x=144+384\\ \Rightarrow24x=528\\ \Rightarrow x=\dfrac{528}{24}=22\)
d)
\(\left(x^2-10\right)\div5=3\\ \Rightarrow\left(x^2-10\right)=3\times5\\ \Rightarrow x^2-10=15\)
\(\Rightarrow x^2=15+10\\ \Rightarrow x^2=25\\ \Rightarrow x^2=5^2\Rightarrow x=5\)
\(2x\left(x+3\right)-3\left(x^2+1\right)=x+1-x\left(x-2\right)\)
\(\Leftrightarrow2x^2+6x-3x^2-3=x+1-x^2+2x\)
\(\Leftrightarrow-x^2+6x-3=-x^2+3x+1\)
\(\Leftrightarrow3x=4\)
hay \(x=\dfrac{4}{3}\)
\(2x\left(x+3\right)-3\left(x^2+1\right)=x+1-x\left(x-2\right)\)
\(\Leftrightarrow2x^2+6x-3x^2-3=x+1-x^2+2x\)
\(\Leftrightarrow3x=4\Leftrightarrow x=\dfrac{4}{3}\)
\(\Leftrightarrow\dfrac{1}{2}x+\dfrac{2}{3}x-x=-4\Leftrightarrow\dfrac{3x+4x-6x}{6}=-\dfrac{24}{6}\)
\(\Rightarrow x=-24\)
b) 50-3(x+4)=14
3(x+4)=36
x+4=13
x=9
c)2⁸‐ⁿ+75=107
2⁸-ⁿ=32
2⁸-ⁿ=2⁵
8-x=5
x=3
Bài 2:
Với x,y,z,t là số tự nhiên khác 0
Có \(\dfrac{x}{x+y+z+t}< \dfrac{x}{x+y+z}< \dfrac{x}{x+y}\)
\(\dfrac{y}{x+y+z+t}< \dfrac{y}{x+y+t}< \dfrac{y}{x+y}\)
\(\dfrac{z}{x+y+z+t}< \dfrac{z}{y+z+t}< \dfrac{z}{z+t}\)
\(\dfrac{t}{x+y+z+t}< \dfrac{t}{x+z+t}< \dfrac{t}{z+t}\)
Cộng vế với vế \(\Rightarrow1< M< \dfrac{x+y}{x+y}+\dfrac{z+t}{z+t}=2\)
=> M không là số tự nhiên.
Bài 1:
Ta có:
\(B=\dfrac{2008}{1}+\dfrac{2007}{2}+\dfrac{2006}{3}+...+\dfrac{2}{2007}+\dfrac{1}{2008}\)
\(B=\left(1+\dfrac{2007}{2}\right)+\left(1+\dfrac{2006}{3}\right)+...+\left(1+\dfrac{2}{2007}\right)+\left(1+\dfrac{1}{2008}\right)+1\)
\(B=\dfrac{2009}{2}+\dfrac{2009}{3}+...+\dfrac{2009}{2007}+\dfrac{2009}{2008}+\dfrac{2009}{2009}\)
\(B=2009.\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2007}+\dfrac{1}{2008}+\dfrac{1}{2009}\right)\)
\(\Rightarrow\dfrac{A}{B}=\dfrac{2009.\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2007}+\dfrac{1}{2008}+\dfrac{1}{2009}\right)}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2007}+\dfrac{1}{2008}+\dfrac{1}{2009}}=2009\)
b ) - 25 + ( - 16 + x ) = 0
( - 16 + x ) = 0 - ( - 25 )
- 16 + x = 25
x = 25 - ( - 16 )
x = 41
Vậy x = 41
\(B=\overline{2x10y9}⋮9\left(0\le x,y\le9\right)\)
\(\Rightarrow\left(2+x+1+0+y+9\right)⋮9\)
\(\Rightarrow\left(12+x+y\right)⋮9\)
Do \(0\le x,y\le9\)
\(\Rightarrow\left[{}\begin{matrix}x+y=6\\x+y=15\end{matrix}\right.\)
\(\Rightarrow\left(x;y\right)\in\left\{\left(1;5\right),\left(5;1\right),\left(2;4\right),\left(4;2\right),\left(3;3\right),\left(6;9\right),\left(9;6\right),\left(8;7\right),\left(7;8\right)\right\}\)
a, Ta có :\(-30+\left(25-x\right)=-1\)
\(\Leftrightarrow\left(-30\right)+25-x=-1\)
\(\Leftrightarrow25-x=\left(-1\right)-\left(-30\right)\)
\(\Leftrightarrow25-x=29\\ \Leftrightarrow x=25-29\)
\(\Leftrightarrow x=\left(-4\right)\)
Vậy \(x=-4\)
b,Ta có :\(\left(x+5\right)+\left(x-9\right)=x+2\)
\(\Leftrightarrow x+5+x-9=x+2\)
\(\Leftrightarrow2.x+\left(5-9\right)=x+2\)
\(\Leftrightarrow\) \(2.x+\left(-4\right)=x+2\)
\(\Leftrightarrow2.x-x=4+2\)
\(\Leftrightarrow x=6\)
Vậy \(x=6\)