Tìm x biết
\(\dfrac{x-69}{30}+\dfrac{x-67}{32}+\dfrac{x-65}{34}=\dfrac{x-63}{36}+\dfrac{x-61}{38}\)
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NK
1
LN
19 tháng 9 2017
\(\)Bạn viết thiếu 1 vế đúng không?
\(\dfrac{x-69}{30}+\dfrac{x-67}{32}+\dfrac{x-65}{34}=\dfrac{x-63}{36}+\dfrac{x-61}{38}+\dfrac{x-59}{40}\)\(\Rightarrow\left(\dfrac{x-69}{30}-1\right)+\left(\dfrac{x-67}{32}-1\right)+\left(\dfrac{x-65}{34}-1\right)=\left(\dfrac{x-63}{36}-1\right)+\left(\dfrac{x-61}{38}-1\right)+\left(\dfrac{x-59}{40}-1\right)\)
\(\Rightarrow\dfrac{x-99}{30}+\dfrac{x-99}{32}+\dfrac{x-99}{34}=\dfrac{x-99}{36}+\dfrac{x-99}{38}+\dfrac{x-99}{40}\)
\(\Rightarrow\dfrac{x-99}{30}+\dfrac{x-99}{32}+\dfrac{x-99}{34}-\dfrac{x-99}{36}-\dfrac{x-99}{38}-\dfrac{x-99}{40}=0\)\(\Rightarrow\left(x-99\right)\left(\dfrac{1}{30}+\dfrac{1}{32}+\dfrac{1}{34}-\dfrac{1}{36}-\dfrac{1}{38}-\dfrac{1}{40}\right)=0\)
Vì \(\dfrac{1}{30}+\dfrac{1}{32}+\dfrac{1}{34}-\dfrac{1}{36}-\dfrac{1}{38}-\dfrac{1}{40}\ne0\)
Nên:
\(x-99=0\Rightarrow x=99\)
DQ
26 tháng 8 2018
a) \(\dfrac{x+43}{57}+\dfrac{x+46}{54}=\dfrac{x+49}{51}+\dfrac{x+52}{48}\)
\(\left(\dfrac{x+43}{57}+1\right)+\left(\dfrac{x+46}{54}+1\right)=\left(\dfrac{x+49}{51}+1\right)+\left(\dfrac{x+52}{48}\right)\)
\(\dfrac{x+43+57}{57}+\dfrac{x+46+54}{54}-\dfrac{x+49+51}{51}-\dfrac{x+52+48}{48}=0\)
\(\dfrac{x+100}{57}+\dfrac{x+100}{54}-\dfrac{x+100}{51}-\dfrac{x+100}{48}=0\)
\(\left(x+100\right)\left(\dfrac{1}{57}+\dfrac{1}{54}-\dfrac{1}{51}-\dfrac{1}{48}\right)=0\)
Mà \(\dfrac{1}{57}+\dfrac{1}{54}-\dfrac{1}{51}-\dfrac{1}{48}\ne0\)
Nên: \(x+100=0\)
\(x=-100\)
VT
2
18 tháng 4 2017
\(\dfrac{x+30}{2007}+\dfrac{x+32}{2005}=\dfrac{x+34}{2003}+\dfrac{x+36}{2001}\)
\(\Leftrightarrow\dfrac{x+30}{2007}+1+\dfrac{x+32}{2005}+1=\dfrac{x+34}{2003}+1+\dfrac{x+36}{2001}+1\)
\(\Leftrightarrow\dfrac{x+2037}{2007}+\dfrac{x+2037}{2005}=\dfrac{x+2037}{2003}+\dfrac{x+2037}{2001}\)
\(\Leftrightarrow\dfrac{x+2037}{2007}+\dfrac{x+2037}{2005}-\dfrac{x+2037}{2003}-\dfrac{x+2037}{2001}=0\)
\(\Leftrightarrow\left(x+2037\right)\left(\dfrac{1}{2007}+\dfrac{1}{2005}-\dfrac{1}{2003}-\dfrac{1}{2001}\right)=0\)
\(\Rightarrow x+2037=0\).Do \(\dfrac{1}{2007}+\dfrac{1}{2005}-\dfrac{1}{2003}-\dfrac{1}{2001}\ne0\)
\(\Rightarrow x=-2037\)
VT
19 tháng 4 2017
Các bạn xem mình làm thế này có đúng không nhé. Nếu sai thì xin các bạn chữa hộ mình
Bài làm
\(\dfrac{x+30}{2007}+\dfrac{x+32}{2005}=\dfrac{x+34}{2003}+\dfrac{x+36}{2001}\)
\(\dfrac{x+30}{2007}+\dfrac{x+32}{2005}-\dfrac{x+34}{2003}-\dfrac{x+36}{2001}=0\)
\(\left(\dfrac{x+30}{2007}+1\right)+\left(\dfrac{x+32}{2005}+1\right)-\left(\dfrac{x+34}{2003}+1\right)-\left(\dfrac{x+36}{2001}+1\right)=0\)
\(\dfrac{x+30+2007}{2007}+\dfrac{x+32+2005}{2005}-\dfrac{x+34+2003}{2003}-\dfrac{x+36+2001}{2001}=0\)\(\dfrac{x+2037}{2007}+\dfrac{x+2037}{2005}-\dfrac{x+2037}{2003}-\dfrac{x+2037}{2001}=0\)\(\left(x+2037\right).\left(\dfrac{1}{2007}+\dfrac{1}{2005}-\dfrac{1}{2003}-\dfrac{1}{2001}\right)=0\)
x+2037=0
x = -2037
30 tháng 4 2017
ta có : \(\dfrac{392-x}{32}+\dfrac{390-x}{34}+\dfrac{388-x}{36}+\dfrac{386-x}{38}\)+\(\dfrac{384-x}{40}=-5\)
\(\Leftrightarrow\)\(\dfrac{392-x}{32}+1+\dfrac{390-x}{34}+1+\dfrac{388-x}{36}+1\)+\(\dfrac{384-x}{40}+1=0\)
\(\Leftrightarrow\)\(\dfrac{424-x}{32}+\dfrac{424-x}{34}+\dfrac{424-x}{36}+\dfrac{424-x}{38}+\dfrac{424-x}{40}=0\)\(\Leftrightarrow\left(424-x\right)\left(\dfrac{1}{32}+\dfrac{1}{34}+\dfrac{1}{36}+\dfrac{1}{38}+\dfrac{1}{40}\right)=0\)
\(\Leftrightarrow x=424\)(vì \(\dfrac{1}{32}+\dfrac{1}{34}+\dfrac{1}{36}+\dfrac{1}{38}+\dfrac{1}{40}\ne0\))
Vậy tập nghiệm của phương trình là s=\(\left\{424\right\}\)
PL
1
12 tháng 9 2017
\(\dfrac{x-1}{65}+\dfrac{x-3}{63}=\dfrac{x-5}{61}+\dfrac{x-7}{59}\)
\(\Leftrightarrow\dfrac{x-1}{65}-1+\dfrac{x-3}{63}-1=\dfrac{x-5}{61}-1+\dfrac{x-7}{59}-1\)
\(\Leftrightarrow\dfrac{x-66}{65}+\dfrac{x-66}{63}=\dfrac{x-66}{61}+\dfrac{x-66}{59}\)
\(\Leftrightarrow\left(x-66\right)\left(\dfrac{1}{65}+\dfrac{1}{63}-\dfrac{1}{61}-\dfrac{1}{59}\right)=0\)
\(\Leftrightarrow x-66=0\)
\(\Leftrightarrow x=66\)
Vậy x=66.
x= 1372221/18559
(x-99) (1/30 + 1/32 + 1/34 - 1/36 - 1/38) = 0
SUy ra x - 99 = 0
VẬy x =99