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Ta có: \(\dfrac{x+1}{99}+\dfrac{x+2}{98}+...+\dfrac{x+50}{50}+50=0\)
\(\Leftrightarrow\dfrac{x+1}{99}+1+\dfrac{x+2}{98}+1+...+\dfrac{x+50}{50}+1=0\)
\(\Leftrightarrow\dfrac{x+100}{99}+\dfrac{x+100}{98}+...+\dfrac{x+100}{50}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\dfrac{1}{99}+\dfrac{1}{98}+...+\dfrac{1}{50}\right)=0\)
mà \(\dfrac{1}{99}+\dfrac{1}{98}+...+\dfrac{1}{50}>0\)
nên x+100=0
hay x=-100
Vậy: S={-100}
\(\dfrac{x+1}{99}+\dfrac{x+2}{98}+...+\dfrac{x+50}{50}+50=0\)
\(\Leftrightarrow\left(\dfrac{x+1}{99}+1\right)+\left(\dfrac{x+2}{98}+1\right)+\left(\dfrac{x+3}{97}+1\right)+...+\left(\dfrac{x+50}{50}+1\right)=0\)
\(\Leftrightarrow\dfrac{x+100}{99}+\dfrac{x+100}{98}+...+\dfrac{x+100}{50}=0\)
\(\Leftrightarrow\left(x+100\right).\left(\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{97}+...+\dfrac{1}{50}\right)=0\)
\(\Leftrightarrow x+100=0\) (vì \(\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{97}+...+\dfrac{1}{50}>0\) )
\(\Leftrightarrow x=-100\)
Ta có:x1+x2+...+x49+x50+x51=(x1+x2)+...+(x49+x50)+x51=0
= 1+1+...+1 +x51=0 (có 25 số 1)
=25 +x51=0
=>x51=0-25= -25
Ta có:x50+x51 =1
x50+(-25)=1
x50 =1-(-25)=26
Vậy x50= 26
Vừa nãy mình viết nhầm
X +1+X+2+X+3+......+X+5=51.25+50
X.50+.....+(1+2+3+.....+50)=51.25+50
X.50+......+[(50.2)+(50.2)]=51.25+50
X.5+....+25.51=51.25+50
--->X.50 =50
--->X=1
Ta có:x1+x2+...+x49+x50+x51=(x1+x2)+...+(x49+x50)+x51=0
= 1 +...+ 1 +x51(có 25 số 1)=0
= 25 +x51=0
=>x51=0-25= -25
Ta có:x50+x51 =1
x50+(-25)=1
x50 =1-(-25)=26
Vậy x50= 26
like cho mình nhang
(x1 + x2) + (x3 + x4) +..... + (x49 + x50) + x51
= 1 + 1+ 1 + .... + 1 + x51 = 0
= 25 + x51 = 0
x51 = 0 - 25
x51 = -25
x1+x2+x3+...+x50+x51=0
=>(x1+x2)+(x3+x4)+...+(x49+x50)+x51=0
=>1+1+1+...+1+x51=0
=>25+x1=0
=>x51=-25
=>x50=1-(-25)=26