Giải pt
x-11/89 + x-13/87 + x-15/85 + x-17/83 =4
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K
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HN
1
VD
19 tháng 3 2022
\(\dfrac{x+11}{89}+\dfrac{x+13}{87}=\dfrac{x+15}{85}+\dfrac{x+17}{83}\\\Leftrightarrow\left(\dfrac{x+11}{89}+1\right)+\left(\dfrac{x+13}{87}+1\right)=\left(\dfrac{x+15}{85}+1\right)+\left(\dfrac{x+17}{83}+1\right)\\ \Leftrightarrow\dfrac{x+100}{89}+\dfrac{x+100}{87}-\dfrac{x+100}{85}-\dfrac{x+100}{83}=0\\ \Leftrightarrow\left(x+100\right)\left(\dfrac{1}{89}+\dfrac{1}{87}-\dfrac{1}{85}-\dfrac{1}{83}\right)=0\\ \Leftrightarrow x+100=0\left(vì\dfrac{1}{89}+\dfrac{1}{87}-\dfrac{1}{85}-\dfrac{1}{83}\ne0\right)\\ \Leftrightarrow x=-100\)
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
PT
2
23 tháng 4 2018
\(\dfrac{x-11}{89}\) +\(\dfrac{x-13}{87}+\dfrac{x-15}{85}+\dfrac{x-17}{83}\)=4
⇔\(\dfrac{x-11}{89}+\dfrac{x-13}{87}+\dfrac{x-15}{85}+\dfrac{x-17}{83}-4=0\)
⇔\(\dfrac{x-11}{89}-1+\dfrac{x-13}{87}-1+\dfrac{x-15}{85}-1+\dfrac{x-17}{83}-1=0\)
⇔\(\dfrac{x-100}{89}+\dfrac{x-100}{87}+\dfrac{x-100}{85}+\dfrac{x-100}{83}=0\)
⇔\(\left(x-100\right)\left(\dfrac{1}{89}+\dfrac{1}{87}+\dfrac{1}{85}+\dfrac{1}{83}\right)=0\)
\(Do\) \(\dfrac{1}{89}+\dfrac{1}{87}+\dfrac{1}{85}+\dfrac{1}{83}\)≠\(0\) nên x-100=0 nên x=100
KL........
JD
23 tháng 4 2018
⇔(\(\dfrac{x-11}{89}\)-1)+(\(\dfrac{x-13}{87}\)-1)+(\(\dfrac{x-15}{85}\)-1)+(\(\dfrac{x-17}{83}\)-1)=0
⇔\(\dfrac{x-100}{89}\)+\(\dfrac{x-100}{87}\)+\(\dfrac{x-100}{85}\)+\(\dfrac{x-100}{83}\)=0
⇔(x-100)(\(\dfrac{1}{89}\)+\(\dfrac{1}{87}\)+\(\dfrac{1}{85}\)+\(\dfrac{1}{83}\))=0 (1)
Do 1/89+1/87+1/85+1/83≠0 nên (1)⇔x-100=0 ⇔x=100
Vậy tập nghiệm của PT là S=\(\left\{100\right\}\)
N
1
2 tháng 7 2016
11+12+13+14+15+16+17+18+19+...+89+88+87+86+85+84+83+82
=( 11 + 89 )+(12+88)+(13+87)+(14+86)+(15+85)+(16+84)+(17+83)+(18+82)+19
=100+100+100+100+100+100+100+100+19
=800+19
=819
15 tháng 6 2016
P = { 13 ; 15 ; 17 ; ... ; 85 ; 87 } có ( 87 - 13 ) : 2 + 1 = 38 ( phần tử)
9 tháng 5 2022
12/13 x 15/16 x 13/15 : 11/16 = 12/13 x 15/16 x 13/15 x 16/11
= 12/11
NT
1
AH
Akai Haruma
Giáo viên
30 tháng 7 2023
Lời giải:
$(x-15)-x.13=0$
$x-15-x.13=0$
$(x-x.13)-15=0$
$x(1-13)-15=0$
$x.(-12)-15=0$
$x.(-12)=15$
$x=15:(-12)=\frac{-5}{4}$
4 tháng 3 2020
\(\frac{x+14}{86}+\frac{x+15}{85}+\frac{x+16}{84}+\frac{x+17}{83}+\frac{x+116}{4}=0\)
\(\Leftrightarrow\frac{x+14}{86}+\frac{x+15}{85}+\frac{x+16}{84}+\frac{x+17}{83}+\frac{x+100}{4}+4=0\)
\(\Leftrightarrow\left(\frac{x+14}{86}+1\right)+\left(\frac{x+15}{85}+1\right)+\left(\frac{x+14}{86}+1\right)+\left(\frac{x+13}{87}+1\right)+\frac{x+100}{4}=0\)
\(\Leftrightarrow\frac{x+100}{86}+\frac{x+100}{85}+\frac{x+100}{84}+\frac{x+100}{83}+\frac{x+100}{4}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4}\right)=0\)
\(\Leftrightarrow x+100=0\left(vì\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4}\ne0\right)\)
\(\Leftrightarrow x=-100\)
vậy.............................
x−1189+x−1387+x−1585+x−1783=4x−1189+x−1387+x−1585+x−1783=4=>(x−1189−1)+(x−1387−1)+(x−1585−1)+(x−1783−1)=0=>(x−1189−1)+(x−1387−1)+(x−1585−1)+(x−1783−1)=0=>x−10089+x−10087+x−10085+x−10083=0=>x−10089+x−10087+x−10085+x−10083=0=>(x−100)(189+187+185+183)=0=>(x−100)(189+187+185+183)=0=> x-100 =0 => x=100Vậy nghiệm là 100
ta có 0=\(\frac{x-11}{89}-1+\frac{x-13}{87}-1+\frac{x-15}{85}-1+\frac{x-17}{83}-1=0\)
0=\(\frac{x-11-89}{89}+\frac{x-13-87}{87}+\frac{x-15-85}{85}+\frac{x-17-83}{83}\)
0=\(\frac{x-100}{89}+\frac{x-100}{87}+\frac{x-100}{85}+\frac{x-100}{83}\)
0=(x-100)(\(\frac{1}{89}+\frac{1}{87}+\frac{1}{85}+\frac{1}{83}\))
vì \(\frac{1}{89}+\frac{1}{87}+\frac{1}{85}+\frac{1}{83}\)khác 0 suy ra x-100=0
x=100