Giải PT \(\frac{x-999}{99}+\frac{x-896}{101}+\frac{x-789}{103}=6\)
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DP
1
25 tháng 3 2020
Ta có : \(\frac{x-999}{99}+\frac{x-896}{101}+\frac{x-789}{103}=6\)
=> \(\frac{x-999}{99}-1+\frac{x-896}{101}-2+\frac{x-789}{103}-3=0\)
=> \(\frac{x-1098}{99}+\frac{x-1098}{101}+\frac{x-1098}{103}=0\)
=> \(\left(x-1098\right)\left(\frac{1}{99}+\frac{1}{101}+\frac{1}{103}\right)=0\)
=> \(x-1098=0\)
=> \(x=1098\)
Vậy phương trình có tập nghiệm là \(S=\left\{1098\right\}\)
DL
1
27 tháng 11 2016
Ta có: \(\frac{x-999}{99}+\frac{x-896}{101}+\frac{x-789}{103}=6\)
\(\Rightarrow\left(\frac{x-999}{99}-1\right)+\left(\frac{x-896}{101}-2\right)+\left(\frac{x-789}{103}-3\right)=6-6\)
\(\Rightarrow\frac{x-1098}{99}+\frac{x-1098}{101}+\frac{x-1098}{103}=0\)
\(\Rightarrow\left(x-1098\right).\left(\frac{1}{99}+\frac{1}{101}+\frac{1}{103}\right)=0\)
Vì \(\frac{1}{99}+\frac{1}{101}+\frac{1}{103}\ne0\)
=> x - 1098 = 0
=> x = 0 + 1098
=> x = 1098
Vậy x = 1098
LH
2
4 tháng 2 2018
\(\dfrac{x-999}{99}+\dfrac{x-896}{101}+\dfrac{x-789}{103}=6\)
\(\Leftrightarrow\dfrac{x-999}{99}-1+\dfrac{x-896}{101}-2+\dfrac{x-789}{103}-3=0\)
\(\Leftrightarrow\dfrac{x-1098}{99}+\dfrac{x-1098}{101}+\dfrac{x-1098}{103}=0\)
\(\Leftrightarrow\left(x-1098\right)\left(\dfrac{1}{99}+\dfrac{1}{101}+\dfrac{1}{103}\right)=0\)
Mà \(\dfrac{1}{99}+\dfrac{1}{101}+\dfrac{1}{103}>0\)
\(\Rightarrow x-1098=0\Leftrightarrow x=1098\)
Vậy x = 1098
14 tháng 1 2018
a, \(\frac{x+1006}{1000}+\frac{x+1007}{999}+\frac{x+1008}{998}+\frac{x+1009}{997}+\frac{x+2022}{4}=0\)
\(\Leftrightarrow\frac{x+1006}{1000}+1+\frac{x+1007}{999}+1+\frac{x+1008}{998}+1+\frac{x+1009}{997}+1+\frac{x+2022}{4}-4=0\)
\(\Leftrightarrow\frac{x+2006}{1000}+\frac{x+2006}{999}+\frac{x+2006}{998}+\frac{x+2006}{997}+\frac{x+2006}{4}=0\)
\(\Leftrightarrow\left(x+2006\right)\left(\frac{1}{1000}+\frac{1}{999}+\frac{1}{998}+\frac{1}{997}+\frac{1}{4}\right)=0\)
Mà \(\frac{1}{1000}+\frac{1}{999}+\frac{1}{998}+\frac{1}{997}+\frac{1}{4}\ne0\)
\(\Rightarrow x+2006=0\Leftrightarrow x=-2006\)
M
4
26 tháng 3 2019
\(\left(\frac{99-x}{101}+1\right)+\left(\frac{97-x}{103}+1\right)+\left(\frac{95-x}{105}+1\right)+\left(\frac{93-x}{107}+1\right)=-4+4\)
\(\frac{200-x}{101}+\frac{200-x}{103}+\frac{200-x}{105}+\frac{200-x}{107}=0\)
\(\left(200-x\right)\left(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\right)=0\) mà \(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\ne0\)
\(\Rightarrow200-x=0\Rightarrow x=200\)
k nha
26 tháng 3 2019
\(\left(\frac{99-x}{101}+1\right)+\left(\frac{97-x}{103}+1\right)+\left(\frac{95-x}{105}+1\right)+\left(\frac{93-x}{107}+1\right)=-4+4\)
\(\frac{110-x}{101}+\frac{110-x}{103}+\frac{110-x}{105}+\frac{110-x}{107}=0\)
\(\left(110-x\right).\left(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\right)=0\)
\(\Rightarrow110-x=0\)( vì \(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\ne0\) )
\(\Rightarrow x=110\)
vậy x=110
10 tháng 3 2020
Cộng 1 vào từng phân số ta sẽ đc
\(\frac{x+100}{99}+\frac{x+100}{98}+\frac{x+100}{97}=\frac{x+100}{101}+\frac{x+100}{102}+\frac{x+100}{103}\)
\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}-\frac{1}{101}-\frac{1}{102}-\frac{1}{103}\right)=0\)
\(\Rightarrow x=-100\)
FC
10 tháng 3 2020
\(\frac{x+1}{99}+\frac{x+2}{98}+\frac{x+3}{97}=\frac{x-1}{101}+\frac{x-2}{102}+\frac{x-3}{103}\)
<=> \(\frac{x+1}{99}+1+\frac{x+2}{98}+1+\frac{x+3}{97}+1=\frac{x-1}{101}+1+\frac{x-2}{102}+1+\frac{x-3}{103}+1\)
<=> \(\frac{x+100}{99}+\frac{x+100}{98}+\frac{x+100}{97}=\frac{x+100}{101}+\frac{x+100}{102}+\frac{x+100}{103}\)
<=> \(\left(x+100\right)\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}-\frac{1}{101}-\frac{1}{102}-\frac{1}{103}\right)=0\)
<=> x + 100 = 0 (vì \(\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}-\frac{1}{101}-\frac{1}{102}-\frac{1}{103}\right)\ne0\))
<=> x = -100
25 tháng 9 2016
\(\frac{x-1}{99}-\frac{x+1}{101}+\frac{x-2}{98}-\frac{x+2}{102}+\frac{x-3}{97}-\frac{x+3}{103}+\frac{x-4}{96}-\frac{x+4}{104}=0\)
\(\Rightarrow\frac{x-1}{99}-1-\frac{x+1}{101}+1+\frac{x-2}{98}-1-\frac{x+2}{102}+1+\frac{x-3}{97}-1-\frac{x+3}{103}+1+\frac{x-4}{96}-1-\frac{x+4}{104}+1=0\)
\(\Rightarrow\frac{x-100}{99}-\frac{x-100}{101}+\frac{x-100}{98}-\frac{x-100}{102}+\frac{x-100}{97}-\frac{x-100}{103}+\frac{x-100}{96}-\frac{x-100}{104}=0\)
\(\Rightarrow\left(x-100\right).\left(\frac{1}{99}-\frac{1}{101}+\frac{1}{98}-\frac{1}{102}+\frac{1}{97}-\frac{1}{103}+\frac{1}{96}-\frac{1}{104}\right)=0\)
Vì \(\frac{1}{99}>\frac{1}{101};\frac{1}{98}>\frac{1}{102};\frac{1}{97}>\frac{1}{103};\frac{1}{96}>\frac{1}{104}\)
\(\Rightarrow\frac{1}{99}-\frac{1}{101}+\frac{1}{98}-\frac{1}{102}+\frac{1}{97}-\frac{1}{103}+\frac{1}{96}-\frac{1}{104}\ne0\)
\(\Rightarrow x-100=0\)
\(\Rightarrow x=100\)
Vậy \(x=100\)
22 tháng 2 2018
Ta có: \(\frac{99-x}{101}+\frac{97-x}{103}+\frac{95-x}{105}+\frac{93-x}{107}=-4\)
\(\Leftrightarrow\frac{99-x}{101}-1+\frac{97-x}{103}-1+\frac{95-x}{105}-1+\frac{93-x}{107}-1=-4+4\)
\(\Leftrightarrow\frac{200-x}{101}+\frac{200-x}{103}+\frac{200-x}{105}+\frac{200-x}{107}=0\)
\(\Leftrightarrow\left(200-x\right).\left(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\right)=0\)
Vì \(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\ne0\)
=> 200 - x = 0
=> x = 200
Vậy x = 200