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a)\(\left(\frac{4}{5}\right)^{2x+7}=\left(\frac{4}{5}\right)^4\)
=> 2x + 7 = 4
2x = 4 - 7
2x = -3
x = -3 : 2
x = -1,5
Vậy x = -1,5
Ta có:
\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{x\left(x+3\right)}=\frac{101}{1540}\)
\(\Rightarrow\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{101}{1540}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{101}{1540}.3=\frac{303}{1540}\)
\(\Rightarrow\frac{1}{x+3}=\frac{1}{5}-\frac{303}{1540}=\frac{1}{308}\)
\(\Rightarrow x+3=308\Leftrightarrow x=305\)
a) \(\frac{x+7}{x+4}=\frac{2}{5}\)
\(\Rightarrow5\left(x+7\right)=2\left(x+4\right)\)
\(\Rightarrow5x+35-2x-8=0\)
\(\Rightarrow3x=-27\)
\(\Rightarrow x=-9\)
b) \(\frac{2x-3}{2}=\frac{50}{2x-3}\)
\(\Rightarrow\left(2x-3\right)^2=100\)
\(\Rightarrow\left[\begin{array}{nghiempt}2x-3=10\\2x-3=-10\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{13}{2}\\x=-\frac{7}{2}\end{array}\right.\)
c) \(\frac{x+1}{x-3}=\frac{x+3}{x+2}\)
\(\Rightarrow\left(x+1\right)\left(x+2\right)=\left(x-3\right)\left(x+3\right)\)
\(\Leftrightarrow x^2+3x+2=x^2-9\)
\(\Leftrightarrow3x=-11\)
\(\Leftrightarrow x=-\frac{11}{3}\)
b, \(3x=2y\Rightarrow\frac{x}{2}=\frac{y}{3}\)
\(7y=5z\Rightarrow\frac{y}{5}=\frac{z}{7}\)
\(\frac{x}{2}=\frac{y}{3};\frac{y}{5}=\frac{z}{7}\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{21}\)
áp dụng dãy tỉ số bằng nhau :
\(\frac{x-y+z}{10-15+21}=\frac{32}{16}=2\)
x = 2 . 10 = 20
y = 2 . 15 = 30
z = 2 . 21 = 42
Vậy : .....
a, \(\frac{x}{3}=\frac{y}{4};\frac{y}{5}=\frac{z}{7}\)
MSC của y là : 20
Có: \(\frac{x}{15}=\frac{y}{20}=\frac{z}{28}\)
Áp dụng dãy tỉ số bằng nhau, ta có:
\(2x+3y-z=186\)
\(\Rightarrow2.15+3.20-28=30+60-28=62\)
\(\frac{186}{62}=3\)
x = 3 . 15 = 45
y = 3 . 20 = 60
z = 3 . 28 = 84
Vậy: .....
Ta có \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\)
\(=\frac{x-1}{2}=\frac{2y-4}{6}=\frac{3z-9}{12}\)
\(=\frac{x-1-\left(2y-4\right)+3z-9}{2-6+12}\)
\(=\frac{x-1-2y+4+3z-9}{8}\)
\(=\frac{\left(x-2y+3z\right)-6}{8}=\frac{14-6}{8}=\frac{8}{8}=1\)
Có \(\frac{x-1}{2}=1\Rightarrow x-1=2\Rightarrow x=3\)
\(\frac{y-2}{3}=1\Rightarrow y-2=3\Rightarrow y=5\)
\(\frac{z-3}{4}=1\Rightarrow z-3=4\Rightarrow z=7\)
\(\frac{1}{4}:x=-\frac{7}{20}\)
\(x=\frac{1}{4}:-\frac{7}{20}\)
\(x=-\frac{5}{7}\)
\(\frac{3}{4}+\frac{1}{4}\div x=\frac{2}{5}\)
\(\Rightarrow\frac{1}{4}\div x=-\frac{7}{20}\)
\(\Rightarrow x=\frac{1}{4}\div\left(-\frac{7}{20}\right)\)
\(\Rightarrow x=-\frac{5}{7}\)