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Ta có:
\(B=115\Rightarrow1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{x}\left(1+2+3+4+...+x\right)=115\)
\(\Leftrightarrow1+\dfrac{1}{2}.\dfrac{3.2}{2}+\dfrac{1}{3}.\dfrac{4.3}{2}+...+\dfrac{1}{x}.\dfrac{\left(1+x\right).x}{2}=115\)
\(\Leftrightarrow\dfrac{1}{2}.2+\dfrac{1}{2}.3+\dfrac{1}{2}.4+...+\dfrac{1}{2}.\left(x+1\right)=115\)
\(\Leftrightarrow\dfrac{1}{2}.\left(1+2+3+4+...+x\right)=115\)
\(\Leftrightarrow\dfrac{1}{2}.\dfrac{\left(x+1\right).x}{2}=115\Rightarrow\dfrac{x.\left(x+1\right)}{4}=115\)
\(\Rightarrow x.\left(x+1\right)=4.115=460\)
Đến đây thì phân tích 460 thành tích của 2 số tự nhiên liên tiếp nhưng ko đc.
\(B=1+\dfrac{1}{2}\left(1+2\right)+...+\dfrac{1}{x}\left(1+2+..+x\right)\)
\(B_x=\dfrac{1}{x}\left(\dfrac{x\left(x+1\right)}{2}\right)=\dfrac{x+1}{2}\)
\(2B=2+3+4+5+...+\left(x+1\right)\)
\(2B+1=1+2+...+\left(x+1\right)=\dfrac{\left(x+1\right)\left(x+2\right)}{2}\)
\(B=115\Leftrightarrow2B+1=231\)
\(\Leftrightarrow\left(x+1\right)\left(x+2\right)=231.2=462\)=21.22
x=20
a) \(\left|3x-\dfrac{1}{2}\right|+\left|\dfrac{1}{4}y+\dfrac{3}{5}\right|=0\)
Do \(\left|3x-\dfrac{1}{2}\right|,\left|\dfrac{1}{4}y+\dfrac{3}{5}\right|\ge0\forall x,y\)
\(\Rightarrow\left\{{}\begin{matrix}3x-\dfrac{1}{2}=0\\\dfrac{1}{4}y+\dfrac{3}{5}=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{1}{6}\\y=-\dfrac{12}{5}\end{matrix}\right.\)
b) \(\left|\dfrac{3}{2}x+\dfrac{1}{9}\right|+\left|\dfrac{5}{7}y-\dfrac{1}{2}\right|\le0\)
Do \(\left|\dfrac{3}{2}x+\dfrac{1}{9}\right|,\left|\dfrac{5}{7}y-\dfrac{1}{2}\right|\ge0\forall x,y\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{3}{2}x+\dfrac{1}{9}=0\\\dfrac{5}{7}y-\dfrac{1}{2}=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{2}{27}\\y=\dfrac{7}{10}\end{matrix}\right.\)
3: \(\left|x-\dfrac{3}{4}\right|-\dfrac{1}{2}=0\)
\(\Leftrightarrow\left|x-\dfrac{3}{4}\right|=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{1}{2}\\x-\dfrac{3}{4}=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{4}\\x=\dfrac{1}{4}\end{matrix}\right.\)
a: \(x=\left(-\dfrac{2}{3}\right)^5:\left(-\dfrac{2}{3}\right)^2=\left(-\dfrac{2}{3}\right)^3=-\dfrac{8}{27}\)
b: =>x-1/2=1/3
=>x=5/6
c: =>2/3x-1=0 hoặc 3/4x+1/2=0
=>x=3/2 hoặc x=-1/2:3/4=-1/2*4/3=-4/6=-2/3
d =>4/9:x=10/3:9/4=10/3*4/9=40/27
=>x=4/9:40/27=4/9*27/40=108/360=3/10
