tim x: x*2 + \(\frac{x}{2}\)=10
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\(\frac{x+2015}{5}+\frac{x+2016}{4}=\frac{x+2017}{3}+\frac{x+2018}{2}\)
\(\Leftrightarrow\left(\frac{x+2015}{5}+1\right)+\left(\frac{x+2016}{4}+1\right)=\left(\frac{x+2017}{3}+1\right)+\left(\frac{x+2018}{2}+1\right)\)
\(\Leftrightarrow\frac{x+2020}{5}+\frac{x+2020}{4}-\frac{x+2020}{3}-\frac{x+2020}{2}=0\)
\(\Leftrightarrow\left(x+2020\right)\left(\frac{1}{5}+\frac{1}{4}-\frac{1}{3}-\frac{1}{2}\right)=0\)
\(\Leftrightarrow x+2020=0\)vì \(\frac{1}{5}+\frac{1}{4}+\frac{1}{3}+\frac{1}{2}\ne0\)
\(\Leftrightarrow x=-2020\)
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\(\Rightarrow5\left(x-10\right)=2\left(x+2\right)\)
\(\Rightarrow5x-50=2x+4\)
\(\Rightarrow3x=54\Rightarrow x=18\)
5x - 50 = 2x + 4
=> 5x - 50 - 2x - 4 = 0
x( 5 - 2 ) - ( 50 + 4 ) = 0
3x - 54 = 0
3x = 54
x = 18
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\(A=\frac{1}{2}\left(\frac{x^{10}}{y^2}+\frac{y^{10}}{x^2}+\right)+\frac{1}{4}\left(x^{16}+y^{16}\right)-x^4y^4-2x^2y^2-1\)
Áp dụng Côsi
\(\frac{1}{2}\left(\frac{x^{10}}{y^2}+\frac{y^{10}}{x^2}\right)\ge\frac{1}{2}.2\sqrt{\frac{x^{10}}{y^2}.\frac{y^{10}}{x^2}}=x^4y^4\)
\(\frac{1}{4}\left(x^{16}+y^{16}+1+1+1+1+1+1\right)\ge\frac{1}{4}.8\sqrt[8]{x^{16}y^{16}}=2x^2y^2\)
\(\Rightarrow A+\frac{6}{4}\ge x^4y^4+2x^2y^2-x^4y^4-2x^2y^2-1=-1\)
\(\Rightarrow A\ge-1-\frac{6}{4}=-\frac{5}{2}\)
Dấu "=" xảy ra khi và chỉ khi \(x^2=y^2=1\)
Vậy GTNN của A là -2,5 khi x2 = y2 = 1
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\(\dfrac{3}{x}=2:\dfrac{9}{10}\Rightarrow\dfrac{3}{x}=\dfrac{20}{9}\Rightarrow x=3:\dfrac{20}{9}=\dfrac{27}{20}\)
\(\dfrac{-2}{\dfrac{3}{x}}=\dfrac{9}{10}\Leftrightarrow x=\dfrac{-2}{3}:\dfrac{9}{10}\Leftrightarrow x=\dfrac{-20}{27}\)
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\(\frac{1}{2}x+\frac{3}{5}x=\frac{-33}{10}\)\(\Leftrightarrow\left(\frac{1}{2}+\frac{3}{5}\right)x=\frac{-33}{10}\)
\(\Leftrightarrow\frac{11}{10}x=\frac{-33}{10}\)\(\Leftrightarrow x=\frac{-33}{10}:\frac{11}{10}=\frac{-33}{10}.\frac{10}{11}=-3\)
Vậy \(x=-3\)
\(\frac{1}{2}\cdot x+\frac{3}{5}\cdot x=-\frac{33}{10}\)
\(\left(\frac{1}{2}+\frac{3}{5}\right)\cdot x=-\frac{33}{10}\)
\(\left(\frac{5}{10}+\frac{6}{10}\right)\cdot x=-\frac{33}{10}\)
\(\frac{11}{10}\cdot x=-\frac{33}{10}\)
\(x=-\frac{33}{10}:\frac{11}{10}=-\frac{33}{10}\cdot\frac{10}{11}\)
\(x=-\frac{33}{11}=-3\)
sua lai dau bai
X x2+X/2=10
\(x\cdot2+\frac{x}{2}=10\)
\(x\cdot\left(2+\frac{1}{2}\right)=10\)
\(x\cdot\frac{5}{2}=10\)
\(x=10:\frac{5}{2}\)
\(x=4\)