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Bài 1:
a, \(\dfrac{x+5}{x}=\dfrac{4}{3}\)
\(\Rightarrow3x+15=4x\\ \Rightarrow4x-3x=15\\ \Rightarrow x=15\)
b, \(\dfrac{x-20}{x-10}=\dfrac{x+40}{x+70}\)
\(\Rightarrow\left(x-20\right).\left(x+70\right)=\left(x+40\right)\left(x-10\right)\)
\(\Rightarrow x^2+70x-20x-1400=x^2-10x+40x-400\)
\(\Rightarrow x^2-x^2+70x-20x+10x-40x=-400+1400\)
\(\Rightarrow20x=1000\Rightarrow x=50\)
c, \(4^x=\dfrac{1.2.3.....31}{4.6.8.....64}\)
\(\Rightarrow4^x=\dfrac{1}{2.2.2.2.....2.2.64}\) (có 30 số 2)
\(\Rightarrow4^x=\dfrac{1}{2^{30}.4^3}\Rightarrow4^x=\dfrac{1}{4^{15}.4^3}\)
\(\Rightarrow4^x=\dfrac{1}{4^{18}}\)
\(\Rightarrow4^x=4^{-18}\)
Vì \(4\ne-1;4\ne0;4\ne1\) nên \(x=-18\)
Chúc bạn học tốt!!!
a , \(\dfrac{x+5}{x}=\dfrac{4}{3}\Leftrightarrow3\left(x+5\right)=4x\)
<=> 3x+15=4x
<=> x= 15
b , \(\dfrac{x-20}{x-10}=\dfrac{x+40}{x+70}\)
<=> \(\dfrac{x-10}{x-10}-\dfrac{10}{x-10}=\dfrac{x+70}{x+70}-\dfrac{30}{x+70}\)
<=> \(1-\dfrac{10}{x-10}=1-\dfrac{30}{x+70}\)
<=> \(\dfrac{10}{x-10}=\dfrac{30}{x+70}\Leftrightarrow\dfrac{1}{x-10}=\dfrac{3}{x+70}\)
<=> (x+70)=3(x-10)
<=> x+70 = 3x-30
<=> 100=2x
<=> x= 50
\(\text{Câu 1: }\\ \text{Theo bài ra ta có : }x+y-z=10\\ \dfrac{x}{2}=\dfrac{y}{3}\Rightarrow\dfrac{x}{2}=\dfrac{4y}{12}\Rightarrow\dfrac{x}{8}=\dfrac{y}{12}\left(1\right)\\ \dfrac{y}{4}=\dfrac{z}{5}\Rightarrow\dfrac{3y}{12}=\dfrac{z}{5}\Rightarrow\dfrac{y}{12}=\dfrac{z}{15}\left(2\right)\\ \text{Từ }\left(1\right)\text{ và }\left(2\right)\text{ suy ra : }\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}\\ \text{ Áp dụng tính chất dãy tỉ số bằng nhau ta được : }\\ \dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{x+y-z}{8+12-15}=\dfrac{10}{5}=2\\ \Rightarrow\left\{{}\begin{matrix}\dfrac{x}{8}=2\Rightarrow x=16\\\dfrac{y}{12}=2\Rightarrow y=24\\\dfrac{z}{15}=2\Rightarrow z=30\end{matrix}\right.\\ \text{Vậy }x=16\\ y=24\\ z=30\)
\(\text{Câu 2 : }\\ \text{Ta có : }\dfrac{x}{2}=\dfrac{y}{5}\\ \Rightarrow\left(\dfrac{x}{2}\right)^2=\left(\dfrac{y}{5}\right)^2=\dfrac{x}{2}\cdot\dfrac{y}{5}=\dfrac{xy}{2\cdot5}=\dfrac{7+3}{10}=\dfrac{10}{10}=1\\ \Rightarrow\left\{{}\begin{matrix}\left(\dfrac{x}{2}\right)^2=1\Rightarrow\dfrac{x}{2}=1\Rightarrow x=2\\\left(\dfrac{y}{5}\right)^2=1\Rightarrow\dfrac{y}{5}=1\Rightarrow y=5\end{matrix}\right.\\ \text{Vậy }x=2\\ y=5\)
Câu 3 : \(\dfrac{\text{Giải}}{ }\)
Gọi số học sinh 4 khối \(6,7,8,9\) lần lượt là \(a;b;c;d\) \(\left(a;b;c;d\in N\text{*}\right)\) \(\left(em\right)\)
Theo bài ra ta có : \(b-d=70\)
\(a;b;c;d\) tỉ lệ với \(9;8;7;6\) \(\Rightarrow\dfrac{a}{9}=\dfrac{b}{8}=\dfrac{c}{7}=\dfrac{d}{6}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được :
\(\dfrac{a}{9}=\dfrac{b}{8}=\dfrac{c}{7}=\dfrac{d}{6}=\dfrac{b-d}{8-6}=\dfrac{70}{2}=35\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{9}=35\Rightarrow a=315\\\dfrac{b}{8}=35\Rightarrow b=280\\\dfrac{c}{7}=35\Rightarrow c=245\\\dfrac{d}{6}=35\Rightarrow d=210\end{matrix}\right.\)
\(\text{Vậy }a=315\\ b=280\\ c=245\\ d=210\)
a, \(-\dfrac{1}{4}-\dfrac{3}{4}:x=-\dfrac{11}{36}\)
\(\Rightarrow\dfrac{3}{4}:x=-\dfrac{1}{4}-\left(-\dfrac{11}{36}\right)=\dfrac{1}{18}\)
\(\Rightarrow x=\dfrac{3}{4}:\dfrac{1}{18}=\dfrac{27}{2}\)
b, \(70:\dfrac{4x+720}{x}=\dfrac{1}{2}\)
\(\Rightarrow\dfrac{4x+720}{x}=140\)
\(\Rightarrow4x+720=140x\Rightarrow140x-4x=720\)
\(\Rightarrow136x=720\Rightarrow x=\dfrac{90}{17}\)
Chúc bạn học tốt!!!
a)\(\dfrac{-1}{4}-\dfrac{3}{4}:x=\dfrac{-11}{36}\)
\(\dfrac{3}{4}:x=\dfrac{-1}{4}-\left(\dfrac{-11}{36}\right)=\dfrac{1}{18}\)
\(\Rightarrow x=\dfrac{3}{4}:\dfrac{1}{18}=\dfrac{27}{2}\)
b)\(70:\dfrac{4x+720}{x}=\dfrac{1}{2}\)
\(\dfrac{4x+720}{x}=70:\dfrac{1}{2}=140\)
\(\Rightarrow4x+720=140x\)
\(\Rightarrow140x-4x=720\)
\(\Rightarrow136x=720\)
\(\Rightarrow x=\dfrac{90}{17}\)
a)\(x=\dfrac{-14\cdot52}{72}\\ x=\dfrac{-91}{9}\)
b)\(x=\dfrac{120\cdot7.2}{70}\\ x=\dfrac{432}{35}\)
c)\(x=\dfrac{2\dfrac{2}{3}\cdot8.5}{5}\\ x=\dfrac{68}{15}\)
d)\(x=\dfrac{4\dfrac{2}{5}\cdot9.5}{8}\\ x=\dfrac{209}{40}\)
a) \(|x+4|=\frac{7}{3}\) \(\Rightarrow x+4=\pm\left(\frac{7}{3}\right)\)
TH1: \(x+4=\frac{7}{3}\)
\(x=\frac{7}{3}-4=-\frac{5}{3}\)
TH2: \(x+4=-\frac{7}{3}\)
\(x=-\frac{7}{3}-4=-\frac{19}{3}\)
Ta có: \(\dfrac{x+2}{5}=\dfrac{y-1}{4}=\dfrac{z-5}{3}\Rightarrow\dfrac{2x+4}{10}=\dfrac{3y-3}{12}=\dfrac{z-5}{3}\)
và 2x-3y+z =70
Áp dụng t/c của dãy tỉ số = nhau ta có:
\(\dfrac{2x+4}{10}=\dfrac{3y-3}{12}=\dfrac{z-5}{3}=\dfrac{2x+4-3y+3+z-5}{10-12+3}=\dfrac{70+2}{1}=72\)
\(\Rightarrow\left\{{}\begin{matrix}2x+4=720\\3y-3=864\\z-5=216\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=358\\y=289\\z=221\end{matrix}\right.\)
Vậy......................
\(a,8^7-2^{18}=2^{21}-2^{18}=2^{17}\left(2^4-2\right)=14.2^7⋮14\)
\(b,10^6-5^7=2^6.5^6-5^7=5^6\left(2^6-5\right)=59.5^6⋮59\)
c ko nói chia hết cho số nào
\(d,3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(=3^{n+1}\left(3^2+3\right)+2^{n+1}\left(2^2+2\right)\)
\(=3^{n+1}.12+2^{n+1}.6\)
\(=6.\left(3^{n+1}.2+2^{n+1}\right)⋮6\)
\(\frac{x+15}{x}=\frac{4}{3}\)
\(\Rightarrow3\left(x+15\right)=4x\)
\(3x+45=4x\)
\(4x-3x=45\)
\(x=45\)
\(\frac{7,5-x}{3,5+x}=\frac{x+40}{x+70}\)
\(\Rightarrow\left(7,5-x\right)\left(x+70\right)=\left(3,5+x\right)\left(x+40\right)\)
\(7,5x+525-x^2-70x=3,5x+140+x^2+40x\)
\(4x+385-2x^2=110x\)
\(385-2x^2=106x\)
Đề sai òi bạn ~ nếu cái đề này thì x = 412372022 ...... số vô tỉ =.= bậc lên cũng cũng không được số hữa tỉ nào auto ...