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\(a,\Leftrightarrow\left[{}\begin{matrix}x-8=0\\x^3+8=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=8\\x^3=-8\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=8\\x=-2\end{matrix}\right.\\ b,\Leftrightarrow4x-3-x-5=30-3x\\ \Leftrightarrow4x-x+3x=30+5+3\\ \Leftrightarrow6x=38\\ \Leftrightarrow x=\dfrac{19}{3}\)
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Viết lại tỉ số ta có : \(\frac{x}{8}=\frac{y}{12}\text{ và }\frac{y}{12}=\frac{z}{15}\)
Áp dụng tính chất của dãy tí số bằng nhau ta có :
\(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)
Vậy\(\hept{\begin{cases}x=8\times2=16\\y=12\times2=24\\z=15\times2=30\end{cases}}\)
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a) ( x - 8 ) ( x3 +8 ) = 0
=> x - 8 = 0 hoặc x3 + 8 = 0
+) x -8 = 0
x = 8
+) x3 + 8 = 0
x3 =-8 ( vô lí )
Vậy x = 8
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\(\frac{x+5}{100}+\frac{x+5}{99}=\frac{x+5}{98}+\frac{x+5}{97}\)
\(\Leftrightarrow\frac{x+5}{100}+\frac{x+5}{99}-\frac{x+5}{98}-\frac{x+5}{97}=0\)
\(\Leftrightarrow\left(x+5\right)\left(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\right)=0\)
\(\Leftrightarrow x+5=0\) (Vì: \(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\ne0\) )
\(\Leftrightarrow x=-5\)
\(\frac{x+5}{100}+\frac{x+5}{99}=\frac{x+5}{98}+\frac{x+5}{97}\)
\(\Rightarrow\frac{x+5}{100}+\frac{x+5}{99}-\frac{x+5}{98}-\frac{x+5}{97}=0\)
\(\Rightarrow\left(x+5\right)\left(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\right)=0\)
Mà \(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\ne0\)
\(\Rightarrow x+5=0\)
\(\Rightarrow x=-5\)
Vậy \(x=-5\)
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a: Ta có: \(\dfrac{x+1}{2}=\dfrac{2}{x+1}\)
\(\Leftrightarrow\left(x+1\right)^2=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=2\\x+1=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)
b: Ta có: \(\dfrac{\left(x-2\right)^2}{7}=\dfrac{49}{\left(x-2\right)}\)
\(\Leftrightarrow x-2=7\)
hay x=9
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a) ta có \(|x+\frac{3}{5}|\ge0\forall x\inℤ\)
\(\Rightarrow C\le0\)
Dấu "=" <=> \(x+\frac{3}{5}=0\Leftrightarrow x=\frac{-3}{5}\)
b) Làm tương tự câu a) được MaxD=\(\frac{3}{14}\)khi \(x=\frac{3}{2}\)
\(\left|x-3\right|+\left|x-5\right|=2\)2
TH1 Nếu \(x\ge5\)thì
\(\left|x-3\right|+\left|x-5\right|=2\)
\(\Leftrightarrow x-3+x-5=2\)
\(\Leftrightarrow2x-8=2\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\)
TH2 Nếu \(x< 5\)thì
\(\left|x-3\right|+\left|x-5\right|=2\)
\(\Leftrightarrow3-x+5-x=2\)
\(\Leftrightarrow-2x+8=2\)
\(\Leftrightarrow-2x=-6\)
\(\Leftrightarrow x=3\)
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Là 3 nha