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\(\frac{x}{y}=\frac{3}{5}\Rightarrow\frac{x}{3}=\frac{y}{5}\) ; \(\frac{y}{z}=\frac{4}{3}\Rightarrow\frac{y}{4}=\frac{z}{3}\)
ta có :
\(\frac{x}{3}=\frac{y}{5}\)
\(\frac{y}{4}=\frac{z}{3}\)
\(\Rightarrow\frac{x}{12}=\frac{y}{20}=\frac{z}{15}\)
áp dụng tính chất dãy tỉ số bằng nhau, ta có :
\(\frac{x}{12}=\frac{y}{20}=\frac{z}{15}=\frac{4x}{48}=\frac{2z}{30}=\frac{4x-y+2z}{48-20+30}=\frac{116}{58}=2\)
\(\frac{x}{12}=3\Rightarrow x=36\)
\(\frac{y}{20}=2\Rightarrow y=40\)
\(\frac{z}{15}=2\Rightarrow z=30\)
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\(B-2x^2y^3z^2+\frac{2}{3}y^4-\frac{1}{5}x^4y^3=A\)
\(\Rightarrow B=A+2x^2y^3-\frac{2}{3}y^4+\frac{1}{5}x^4y^3\)
\(\Rightarrow B=-4x^5y^3+x^4y^3\cdot3x^2y^3z^2+4x^5y^3+x^2y^3z^2-2y^4+2x^2y^3z^2-\frac{2}{3}y^4+\frac{1}{5}x^4y^3\)
\(=\left(-4x^5y^3+4x^5y^3\right)+\left(x^2y^3z^2+2x^2y^3z^2\right)+x^4y^3\cdot3x^2y^3z^2-\left(2y^4+\frac{2}{3}y^4\right)-\frac{1}{5}x^4y^3\)
\(=3x^2y^3z^2+x^4y^3\cdot3x^2y^3z^2-\frac{8}{6}y^4-\frac{1}{5}x^4y^3\)
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a) ta có: \(-3x=5y\Rightarrow\frac{x}{5}=\frac{y}{-3}\)
ADTCDTSBN
có: \(\frac{y}{-3}=\frac{x}{5}=\frac{y-x}{-3-5}=\frac{20}{-8}=\frac{5}{2}\)
=> y/-3 = 5/2 => y = -15/2
x/5 = 5/2 => x = 25/2
KL:...
b) ta có: \(\frac{2x}{3}=\frac{3y}{4}\Rightarrow8x=9y\Rightarrow\frac{x}{9}=\frac{y}{8}\)
\(\frac{3y}{4}=\frac{4z}{5}\Rightarrow15y=8z\Rightarrow\frac{y}{8}=\frac{z}{15}\)
\(\Rightarrow\frac{x}{9}=\frac{y}{8}=\frac{z}{15}\)
ADTCDTSBN
có: \(\frac{x}{9}=\frac{y}{8}=\frac{z}{15}=\frac{x+y+z}{9+8+15}=\frac{49}{32}\)
=> x/9 = 49/32 => x = ...
...
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A=1+(2-3-3+5)+(6-7-8+9)+....+(98-99-100+101)+102
=1+0+0+....+102=103
b) |1-2x|>7
=> 1-2x>7 hoặc 1-2x<-7
=> 2x<-6 hoặc 2x>8
=> x<-3 hoặc x>4
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\(\frac{7^{x+2}+7^{x+1}+7x}{57}=\frac{5^{2x}+5^{2x+1}+5^{2x+3}}{131}\)
\(\Rightarrow\frac{7x\left(7^2+7^1+1\right)}{57}=\frac{5^{2x}\left(1+5^1+5^3\right)}{131}\)
\(\Rightarrow\frac{7x\left(49+7+1\right)}{57}=\frac{5^{2x}\left(1+5+125\right)}{131}\)
\(\Rightarrow\frac{7x.57}{57}=\frac{5^{2x}.131}{131}\)
\(\Rightarrow7x=25x\)
\(\Rightarrow x=0\)
\(\left(4x-3\right)^4=\left(4x-3\right)^2\)
\(\Rightarrow\left(4x-3\right)^4-\left(4x-3\right)^2=0\)
\(\Rightarrow\left(4x-3\right)^2\left[\left(4x-3\right)^2-1\right]=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(4x-3\right)^2=0\\\left(4x-3\right)^2=1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}4x-3=0\\4x-3=-1\\4x-3=1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=\frac{3}{4}\\x=\frac{1}{2}\\x=1\end{cases}}\)
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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
\(\frac{5-2x}{3}=\frac{4x-1}{-5}\)
\(\Leftrightarrow\left(5-2x\right).-5=\left(4x-1\right).3\)
\(\Leftrightarrow-25+10x=12x-3\)
\(\Leftrightarrow-25+10x-12x+3=0\)
\(\Leftrightarrow-22-2x=0\)
\(\Leftrightarrow-2x=22\)
\(\Leftrightarrow x=-11\)
Vậy: \(x=-11\)