Tìm x biết :
\(\frac{x-11}{95}+\frac{x-13}{93}=\frac{x-15}{91}+\frac{x-17}{89}\)
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4 tháng 2 2017
Phương trình 1:
\(\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}=10\)
\(\Rightarrow\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}-10=0\)
\(\Rightarrow\left(\frac{x-85}{15}-1\right)+\left(\frac{x-74}{13}-2\right)+\left(\frac{x-67}{11}-3\right)+\left(\frac{x-64}{9}-4\right)=0\)
\(\Rightarrow\frac{x-85-15}{15}+\frac{x-74-26}{13}+\frac{x-67-33}{11}+\frac{x-64-36}{9}=0\)
\(\Rightarrow\frac{x-100}{15}+\frac{x-100}{13}+\frac{x-100}{11}+\frac{x-100}{9}=0\)
\(\Rightarrow\left(x-100\right)\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)=0\)
Do \(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\ne0\)
\(\Rightarrow x-100=0\)
\(\Rightarrow x=100\)
Vậy x = 100.
4 tháng 2 2017
Phương trình 3:
\(\frac{1909-x}{91}+\frac{1907-x}{93}+\frac{1905-x}{95}+\frac{1903-x}{97}+4=0\)
\(\Rightarrow\left(\frac{1909-x}{91}+1\right)+\left(\frac{1907-x}{93}+1\right)+\left(\frac{1905-x}{95}+1\right)+\left(\frac{1903-x}{97}+1\right)=0\)
\(\Rightarrow\frac{1909-x+91}{91}+\frac{1907-x+93}{93}+\frac{1905-x+95}{95}+\frac{1903-x+97}{97}=0\)
\(\Rightarrow\frac{2000-x}{91}+\frac{2000-x}{93}+\frac{2000-x}{95}+\frac{2000-x}{97}=0\)
\(\Rightarrow\left(2000-x\right)\left(\frac{1}{91}+\frac{1}{93}+\frac{1}{95}+\frac{1}{97}\right)=0\)
Do \(\frac{1}{91}+\frac{1}{93}+\frac{1}{95}+\frac{1}{97}\ne0\)
\(\Rightarrow2000-x=0\)
\(\Rightarrow x=2000\)
Vậy x = 2000.
8 tháng 4 2019
\(\frac{x+5}{95}+\frac{x+6}{94}+\frac{x+7}{93}+\frac{x+8}{92}+\frac{x+9}{91}=-5\)
\(\left(\frac{x+5}{95}+1\right)+\left(\frac{x+6}{94}+1\right)+\left(\frac{x+7}{93}+1\right)+\left(\frac{x+8}{92}+1\right)+\left(\frac{x+9}{91}+1\right)=-5+5=0\)
2 tháng 2 2017
(109-x)/91+(107-x)/93+(105-x)/95+(103-x)/97=-4
[(109-x)/91 +1]+[(107-x)/93 +1]+[(105-x)/95 +1]+[(103-x)/97 +1]-4=-4
(109+91-x)/91+(107+93-x)/93+(105+95-x)/95+(103+97-x)/97=-4+4
(200-x)/91+(200-x)/93+(200-x)/95+(200-x)/97=0
(200-x)(1/91+1/93+1/95+1/97)=0
Ma : 1/91+1/93+1/95+1/97\(\ne\)0
=>200-x=0
=>x=200
3 tháng 4 2016
(x+2)/17+(x+4)/15+(x+6)/13=(x+8)/11+(x+10)/9+(x+12)/7
=>(x+2+17)/17+(x+4+15)/15+(x+6+13)/13=(x+8+11)/11+(x+10+9)/9+(x+12+7)/7
=>(x+19)/17+(x+19)/15+(x+19)/13=(x+19)/11+(x+19)/9+(x+19)/7
=>(x+19)/17+(x+19)/15+(x+19)/13-(x+19)/11-(x+19)/9-(x+19)/7=0
=>(x+19)*(1/17+1/15+1/13-1/11-1/9-1/7)=0
=>x+19=0
=>x=19
TN
3 tháng 4 2016
áp dụng tc tỉ lệ thức ta có :
\(\Leftrightarrow\frac{671x+2804}{3315}=\frac{239x+2462}{693}\Rightarrow\left(671x+2804\right)693=3315\left(239x+2462\right)\)
=>(671x+2804)693=693(671x+2804) (VT)
<=>693(671x+2804)=3315(239x+2462)
=>465003x+1943172=792285x+8161530
=>-327282x=621835
=>x=621835:(-327282)
=>x=-19
16 tháng 5 2016
b) \(\frac{x-11}{89}+\frac{x-13}{87}+\frac{x-15}{85}+\frac{x-17}{83}=4\)
\(=>\left(\frac{x-11}{89}-1\right)+\left(\frac{x-13}{87}-1\right)+\left(\frac{x-15}{85}-1\right)+\left(\frac{x-17}{83}-1\right)=0\)
\(=>\frac{x-100}{89}+\frac{x-100}{87}+\frac{x-100}{85}+\frac{x-100}{83}=0\)
\(=>\left(x-100\right)\left(\frac{1}{89}+\frac{1}{87}+\frac{1}{85}+\frac{1}{83}\right)=0\)
=> x-100 =0 => x=100
Vậy nghiệm là 100
NT
1
1 tháng 2 2018
<=> (1927-x/91 + 1)+(1925-x/93 + 1) + (1923-x/95 + 1) + (1921-x/97 + 1) = 0
<=> 2018-x/91 + 2018-x/93 + 2018-x/95 + 2018-x/97 = 0
<=> (2018-x).(1/91 + 1/93 + 1/95 + 1/97) = 0
<=> 2018-x = 0 ( vì 1/91 + 1/93 + 1/95 + 1/97 > 0 )
<=> x = 2018
Vậy x = 2018
Tk mk nha
TN
24 tháng 11 2016
\(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)
\(\Leftrightarrow\frac{x+1}{94}+1+\frac{x+2}{93}+1+\frac{x+3}{92}+1=\frac{x+4}{91}+1+\frac{x+5}{90}+1+\frac{x+6}{89}+1\)
\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}=\frac{x+95}{91}+\frac{x+95}{90}+\frac{x+95}{89}\)
\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}-\frac{x+95}{91}-\frac{x+95}{90}-\frac{x+95}{89}=0\)
\(\Leftrightarrow\left(x+95\right)\left(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\right)=0\)
\(\Leftrightarrow x+95=0\).Do \(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\ne0\)
\(\Leftrightarrow x=-95\)
TT
10 tháng 1 2017
(x+1)/94 + ( x+2)/93 + ( x+3)/92.......
= ................ + ( x+6)/89
<=> (x+1)/94 + 1 + ( x+2)/93 +1 .........
=.............. cộng 1 nhá
<=> (x+95)/94 + ( x+96) / 93 + ( x+95)/92
= ( x+95)/91 + ( x+95)/90 + ( x+95)/89
<=> ( x+95) ( 1/94 +1/93 +1/92 )
= ( x+95) ( 1/91 +1/90 +1/89)
<=> ( x+95) ( 1/94 +1/93 +1/92 - 1/91 - 1/90 - 1/89 )
<=> x+95 =0
<=>x = -95
Vậy :x = -95
29 tháng 6 2016
a)\(\frac{x}{108}=\frac{-7}{9}.\frac{5}{6}\)
\(\frac{x}{108}=\frac{-35}{54}\)
\(\frac{x}{108}=\frac{-70}{108}\)
\(x=-70\)
b)
\(\frac{x-11}{95}+\frac{x-13}{93}=\frac{x-15}{91}+\frac{x-17}{89}\) => \(\frac{x-11}{95}-1+\frac{x-13}{93}-1=\frac{x-15}{91}-1+\frac{x-17}{89}-1\)
=>\(\frac{x-106}{95}+\frac{x-106}{93}=\frac{x-106}{91}+\frac{x-106}{89}\)
=>\(\left(\frac{1}{95}+\frac{1}{93}\right)\left(x-106\right)-\left(\frac{1}{91}+\frac{1}{89}\right)\left(x-106\right)=0\)
<=>\(\left[\left(\frac{1}{95}+\frac{1}{93}\right)-\left(\frac{1}{91}+\frac{1}{89}\right)\right]\left(x-106\right)=0\).Vì\(\frac{1}{95}< \frac{1}{91};\frac{1}{93}< \frac{1}{89}\) nên\(\frac{1}{95}+\frac{1}{93}< \frac{1}{91}+\frac{1}{89}\)
=>\(\left(\frac{1}{95}+\frac{1}{93}\right)-\left(\frac{1}{91}+\frac{1}{89}\right)< 0\) hay khác 0.Vậy x - 106 = 0, tìm được x = 106