tìm x biết x + 2x+ 3x + 4x +....+ 2016x = 2017.2018
VIOLYMPIC TOÁN 7 NHAK
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=>(1+2+3+......+2016).x=4070306
=>2033136.x=4070306
=>x=4070306:2033136
=>x=\(\frac{1009}{504}\)
=> (x + x + x + .... + x) . (1 + 2 + 3 + ..... + 2016) = 2017.2018
=> 2016x . 1008 . 2017 = 2017 . 2018
=> 2016x . 1008 = 2018
=> /////////////
1) \(x+2\cdot x+3\cdot x+4\cdot x+...+2016\cdot x=2016\cdot2017\)
\(=x\cdot\left(2+3+4+...+2016\right)=4066272\)
\(=x\cdot2033136=4066272\)
\(\Rightarrow x=\frac{4066272}{2033136}=2\)
2) \(x-2\cdot x+3\cdot x-4\cdot x+...-2016\cdot x=2016\cdot2017\)
\(x\cdot\left\{\left(-2+\left(-4\right)+\left(-6\right)+...+\left(-2016\right)\right)+\left(1+3+5+7+...+2015\right)\right\}=4066272\)
\(x\cdot\left\{\left(-1017072\right)+1016064\right\}=4066272\)
\(x\cdot\left(-1008\right)=4066272\)
\(\Rightarrow x=-\frac{4066272}{1008}=-4034\)
x(1+2+3...2016)=2017.2018
x.2017.2016:2=2017.2018
1008x=2018
x=1009/504
Tìm x biết
1. 2(5x-8)-3(4x-5)=4(3x-4)+11
2. (2x+1)2-(4x-1).(x-3)-15=0
3. (3x-1).(2x-7)-(1-3x).(6x-5)=0
1) \(\Rightarrow10x-16-12x+15=12x-16+11\)
\(\Rightarrow14x=4\Rightarrow x=\dfrac{2}{7}\)
2) \(\Rightarrow4x^2+4x+1-4x^2+13x-3-15=0\)
\(\Rightarrow17x=17\Rightarrow x=1\)
3) \(\Rightarrow\left(3x-1\right)\left(2x-7+6x-5\right)=0\)
\(\Rightarrow\left(2x-3\right)\left(3x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)
2: Ta có: \(\left(2x+1\right)^2-\left(4x-1\right)\left(x-3\right)-15=0\)
\(\Leftrightarrow4x^2+4x+1-4x^2+12x+x-3-15=0\)
\(\Leftrightarrow17x=17\)
hay x=1