9.x - 109 = 27
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Khách
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1 tháng 3 2017
\(\left(\frac{x+14}{200}+1\right)+\left(\frac{x+27}{187}+1\right)+\left(\frac{x+105}{109}+1\right)=\left(\frac{x+200}{14}+1\right)\)
\(+\left(\frac{x+187}{27}+1\right)+\left(\frac{x+109}{105}+1\right)\)
\(\Rightarrow\frac{x+214}{200}+\frac{x+214}{187}+\frac{x+214}{109}-\frac{x+214}{14}-\frac{x+214}{27}-\frac{x+214}{105}=0\)
\(\Rightarrow\left(x+214\right)\left(\frac{1}{200}+\frac{1}{187}+\frac{1}{109}-\frac{1}{14}-\frac{1}{27}-\frac{1}{105}\right)=0\)
Mà \(\frac{1}{200}+\frac{1}{187}+\frac{1}{109}-\frac{1}{14}-\frac{1}{27}-\frac{1}{105}\ne0\)
\(\Rightarrow x+214=0\)
\(\Rightarrow x=-214\)
Vậy x = -214
18 tháng 2 2020
\(\Leftrightarrow\frac{x+14}{200}+\frac{x+27}{187}+\frac{x+105}{109}-\frac{x+200}{14}-\frac{x+187}{27}-\frac{x+109}{105}=0\)
\(\Leftrightarrow\left(\frac{x+14}{200}+1\right)+\left(\frac{x+27}{187}+1\right)+\left(\frac{x+105}{109}+1\right)-\left(\frac{x+200}{14}+1\right)-\left(\frac{x+187}{27}+1\right)-\left(\frac{x+109}{105}+1\right)=0\)\(\Leftrightarrow\frac{x+214}{200}+\frac{x+214}{187}+\frac{x+214}{109}-\frac{x+214}{14}-\frac{x+214}{27}-\frac{x+214}{105}=0\)
\(\Leftrightarrow\left(x+214\right)\left(\frac{1}{200}+\frac{1}{187}+\frac{1}{109}-\frac{1}{14}-\frac{1}{27}-\frac{1}{105}\right)=0\)
Mà \(\frac{1}{200}+\frac{1}{187}+\frac{1}{109}< \frac{1}{14}+\frac{1}{27}+\frac{1}{105}\Rightarrow\frac{1}{200}+\frac{1}{187}+\frac{1}{109}-\frac{1}{14}-\frac{1}{27}-\frac{1}{105}\ne0\)
\(\Rightarrow x+214=0\)
\(\Rightarrow x=-214\)
Vậy x=-214
HY
18 tháng 2 2020
\(\frac{x+14}{200}+\frac{x+27}{187}+\frac{x+105}{109}=\frac{x+200}{14}+\frac{x+187}{27}+\frac{x+109}{105}\\\Leftrightarrow \frac{x+14}{200}+1+\frac{x+27}{187}+1+\frac{x+105}{109}+1=\frac{x+200}{14}+1+\frac{x+187}{27}+1+\frac{x+109}{105}+1\\\Leftrightarrow \frac{x+214}{200}+\frac{x+214}{187}+\frac{x+214}{109}-\frac{x+214}{14}-\frac{x+214}{27}-\frac{x+214}{105}=0\\\Leftrightarrow \left(x+214\right)\left(\frac{1}{200}+\frac{1}{187}+\frac{1}{109}-\frac{1}{14}-\frac{1}{27}-\frac{1}{105}\right)=0\)
\(\Leftrightarrow x+214=0\left(vi\frac{1}{200}+\frac{1}{187}+\frac{1}{109}-\frac{1}{14}-\frac{1}{27}-\frac{1}{105}\ne0\right)\\\Leftrightarrow x=-214 \)
Vậy tập nghiệp của phương trình trên là \(S=\left\{-214\right\}\)
JS
17 tháng 2 2020
Giải:
Ta có:
\(\frac{x+1}{15}+\frac{x+2}{7}+\frac{x+4}{4}+6=0\)
\(\Leftrightarrow\frac{x}{15}+\frac{1}{15}+\frac{x}{7}+\frac{2}{7}+\frac{x}{4}+\frac{4}{4}+6=0\)
\(\Leftrightarrow\frac{x}{15}+\frac{x}{7}+\frac{x}{4}=-\frac{772}{105}\)
\(\Leftrightarrow x\left(\frac{1}{15}+\frac{1}{7}+\frac{1}{4}\right)=-\frac{772}{105}\)
\(\Leftrightarrow x=-16\)
Vậy phương trình trên có nghiệm là x = -16.
b. Cách làm tương tự.
Chúc bạn học tốt@@
24 tháng 8 2020
Pt <=> \(\left(\frac{x+14}{200}+1\right)+\left(\frac{x+27}{187}+1\right)+\left(\frac{x+105}{109}+1\right)=\left(\frac{x+200}{14}+1\right)+\left(\frac{x+187}{27}+1\right)+\left(\frac{x+109}{105}+1\right)\)<=> \(\frac{x+14+200}{200}+\frac{x+27+187}{187}+\frac{x+105+109}{109}=\frac{x+200+14}{14}+\frac{x+187+27}{27}+\frac{x+109+105}{105}\)<=> \(\frac{x+214}{200}+\frac{x+214}{187}+\frac{x+214}{109}=\frac{x+214}{14}+\frac{x+214}{27}+\frac{x+214}{105}\)
<=> \(\frac{x+214}{200}+\frac{x+214}{187}+\frac{x+214}{109}-\frac{x+214}{14}-\frac{x+214}{27}-\frac{x+214}{105}=0\)
<=> \(\left(x+214\right)\left(\frac{1}{200}+\frac{1}{187}+\frac{1}{109}-\frac{1}{14}-\frac{1}{27}-\frac{1}{105}\right)=0\)
Vì \(\left(\frac{1}{200}+\frac{1}{187}+\frac{1}{109}-\frac{1}{14}-\frac{1}{27}-\frac{1}{105}\right)\ne0\)
<=> \(x+214=0\)
<=> \(x=-214\)
NC
24 tháng 8 2020
Ta có:
\(\frac{x+14}{200}+\frac{x+27}{187}+\frac{x+105}{109}=\frac{x+200}{14}+\frac{x+187}{27}+\frac{x+109}{105}\)
Cộng thêm mỗi phân thức 1 ta được:
\(\frac{x+214}{200}+\frac{x+214}{187}+\frac{x+214}{109}-\frac{x+214}{14}-\frac{x+214}{27}-\frac{x+214}{105}=0\)
\(\Leftrightarrow x+214=0\Rightarrow x=-214\)
QN
14 tháng 7 2018
\(1-\left(\frac{59}{9}+x-\frac{114}{18}\right):\frac{109}{9}=0\)
\(1-\left(\frac{59}{9}+x-\frac{114}{18}\right)=0\)
\(\frac{59}{9}+x-\frac{114}{18}=1\)
\(x-\frac{114}{18}=\frac{-50}{9}\)
\(x=\frac{7}{9}\)
Vậy \(x=\frac{7}{9}\)
S
15 tháng 5 2017
a, 810 - 89 - 88 = 88(82 - 8 - 1) = 88.55 chia hết cho 55
b, 76 + 75 - 74 = 74(72 + 7 - 1) = 74.55 = 74.5.11 chia hết cho 11
c, 817 - 279 - 913 = 328 - 327 - 326 = 324(34 - 33 - 32) = 324.45 chia hết cho 45
d, 109 + 108 + 107 = 106(103 + 102 + 10) = 106.1110 = 106.2.555 chia hết cho 555
NT
1
\(x=27+109\\ x=136\)