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18 tháng 3 2023
\(\Leftrightarrow\dfrac{16}{x+4}+\dfrac{16}{x-4}=\dfrac{5}{3}\)
=>\(\dfrac{16x-64+16x+64}{x^2-16}=\dfrac{5}{3}\)
=>5(x^2-16)=3*32x=96x
=>5x^2-96x-80=0
=>x=20 hoặc x=-4/5
19 tháng 3 2023
nếu là giải PT bằng cách quy đồng:
25x2 + 480 - 400 = 0
làm sao để phan tích ra ạ.
4 tháng 4 2020
\(\frac{80}{x+4}+\frac{80}{x-4}=\frac{25}{3}\left(ĐkXĐ:x\ne\pm4\right)\\ \Leftrightarrow\frac{3.80\left(x-4\right)+3.80\left(x+4\right)-25.\left(x^2-16\right)}{\left(x^2-16\right).3}=0\\ \Leftrightarrow\frac{240x-960+240x+960-25x^2+400}{3.\left(x^2-16\right)}=0\\ \Leftrightarrow\frac{-25x^2+480x+400}{3.\left(x^2-16\right)}=0\\ \Leftrightarrow\frac{-25.\left(x+\frac{4}{5}\right)\left(x-20\right)}{3.\left(x^2-16\right)}=0\\ \Leftrightarrow\left[{}\begin{matrix}x+\frac{4}{5}=0\\x-20=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\frac{4}{5}\left(Nhận\right)\\x=20\left(Nhận\right)\end{matrix}\right.\\ \Rightarrow S=\left\{-\frac{4}{5};20\right\}\)
25 tháng 2 2019
\(\frac{x+5}{95}+\frac{x+3}{97}+\frac{x+1}{99}=\frac{x+15}{85}+\frac{x+20}{80}+\frac{x+25}{75}.\)
\(\frac{x+5}{95}+1+\frac{x+3}{97}+1+\frac{x+1}{99}+1-\frac{x+15}{85}-1-\frac{x+20}{80}-1-\frac{x+25}{75}-1=0\)
\(\frac{x+100}{95}+\frac{x+100}{97}+\frac{x+100}{99}-\frac{x+100}{85}-\frac{x+100}{80}-\frac{x+100}{75}=0\)
\(\left(x+100\right).\left(\frac{1}{95}+\frac{1}{97}+\frac{1}{99}-\frac{1}{85}-\frac{1}{80}-\frac{1}{75}\right)=0\)
\(\Rightarrow x+100=0\Rightarrow x=-100\)
\(\frac{1}{95}+\frac{1}{97}+\frac{1}{99}-\frac{1}{85}-\frac{1}{80}-\frac{1}{75}\ne0\)
DU
2
12 tháng 3 2020
\(\frac{x-90}{10}+\frac{x-85}{15}=\frac{x-80}{20}+\frac{x-75}{25}\)
<=> \(\left(\frac{x-90}{10}-1\right)+\left(\frac{x-85}{15}-1\right)=\left(\frac{x-80}{20}-1\right)+\left(\frac{x-75}{25}-1\right)\)
<=> \(\frac{x-100}{10}+\frac{x-100}{15}=\frac{x-100}{20}+\frac{x-100}{25}\)
<=> (x - 100)(1/10 + 1/15 - 1/20 - 1/25) = 0
<=> x - 100 = 0
<=> x = 100
Vậy S = {100}
19 tháng 11 2021
noooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
NC
0
18 tháng 1 2016
a, <=> (x-5/100) -1 +(x-4/101) -1 +(x-3/102) -1= (x-100/5) -1+(x-101/4) -1 +(x-102/3) -1
<=> (x-105)(1/100 +1/101 +1/102)= (x-105)(1/5+1/4+1/3)
<=> (x-105)(1/100+1/101+1/102-1/5-1/4-1/3)=0
vì 1/100+1/101+1/102-1/5-1/4-1/3 khác 0 <=> x-105=0
<=> x=105
18 tháng 1 2016
b, 29-x/21 +1+27-x/23 +1+25-x/25 +1+23-x/27 +1+21-x/29 +1=0
<=> 50-x/21 +50-x/23 +50-x/25 +50-x/27 +50-x/29=0
<=> (50-x)(1/21 +1/23 +1/25 +1/27 +1/29)=0
vì 1/21+1/23+1/25+1/27+1/29 lớn hơn 0
nên 50-x=0
<=> x=50
LH
2
27 tháng 1 2016
\(\frac{x-17}{33}+\frac{169-x}{23}+\frac{x}{25}=4\)
\(\Rightarrow575.\left(x-17\right)+825.\left(169-x\right)+759x=75900\)
\(\Rightarrow575x-9775+139425-825x+759x-75900=0\)
\(\Rightarrow509x=-53750\)
\(\Rightarrow x=\frac{-53750}{509}\)
TN
27 tháng 1 2016
sử dụng tỉ lệ con nhà bà thức ta có (:|
\(\Leftrightarrow\frac{509x+129650}{18975}=\frac{4}{1}\Rightarrow\left(509x+129650\right)1=18975.4\)
\(\Rightarrow\frac{\left(509x+129650\right)1}{509x}=\frac{18975.4}{509x}\)
\(\Rightarrow\frac{509x+129650}{509x}=\frac{18975.4}{509x}\)
\(\Rightarrow x=-105,599214145383\)
\(\frac{80}{x+4}+\frac{80}{x-4}=\frac{25}{3}\left(1\right)\)
ĐKXĐ: \(x\ne\pm4\)
\(\left(1\right)\Leftrightarrow\frac{80\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}+\frac{80\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}=\frac{25}{3}\)
\(\Leftrightarrow\frac{80x-320+80x+320}{\left(x-4\right)\left(x+4\right)}=\frac{25}{3}\)
\(\Leftrightarrow\frac{160x}{\left(x-4\right)\left(x+4\right)}=\frac{25}{3}\)
\(\Rightarrow480x=25\left(x-4\right)\left(x+4\right)\)
\(\Leftrightarrow480x=25\left(x^2-16\right)\)
\(\Leftrightarrow480x=25x^2-400\)
\(\Leftrightarrow25x^2-480x-400=0\)
\(\Leftrightarrow25x^2-480x+2304-2704=0\)
\(\Leftrightarrow\left(5x-48\right)^2=2704\)
\(\Leftrightarrow\left|5x-48\right|=52\)
+Trường hợp 1: Nếu \(x\ge\frac{48}{5}\)thì \(5x-48\ge0\Rightarrow\left|5x-48\right|=5x-48\)
Ta có phương trình;
\(5x-48=52\)
\(\Leftrightarrow5x=100\)
\(\Leftrightarrow x=20\)(thỏa măn)
+Trường hợp 2: Nếu\(x< \frac{48}{5}\)thì \(5x-48< 0\Rightarrow\left|5x-48\right|=48-5x\)
Ta có phương trình:
\(48-5x=52\)
\(\Leftrightarrow-5x=4\)
\(\Leftrightarrow x=-\frac{4}{5}\)(thỏa mãn)
\(S=\left\{20;-\frac{4}{5}\right\}\)
Ta có: \(\frac{80}{x+4}+\frac{80}{x-4}=\frac{25}{3}\)
\(\Leftrightarrow80.\left[\frac{x-4+x+4}{\left(x+4\right).\left(x-4\right)}\right]=\frac{25}{3}\)
\(\Leftrightarrow\frac{2x}{x^2-16}=\frac{25}{3}:80\)
\(\Leftrightarrow\frac{2x}{x^2-16}=\frac{5}{48}\)
\(\Rightarrow48.2x=5.\left(x^2-16\right)\)
\(\Leftrightarrow96x=5x^2-80\)
\(\Leftrightarrow5x^2-96x-80=0\)
\(\Leftrightarrow\left(5x^2-100x\right)+\left(4x-80\right)=0\)
\(\Leftrightarrow5x.\left(x-20\right)+4.\left(x-20\right)=0\)
\(\Leftrightarrow\left(5x+4\right).\left(x-20\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}5x+4=0\\x-20=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}5x=-4\\x=20\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{4}{5}\left(TM\right)\\x=20\left(TM\right)\end{cases}}\)
Vậy \(S=\left\{-\frac{4}{5};20\right\}\)