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1) Ta có : \(\frac{x}{5}=\frac{y}{4}=\frac{2x}{10}=\frac{2x+y}{10+4}=\frac{28}{14}=2\)
Nên : \(\frac{x}{5}=2\Rightarrow x=10\)
\(\frac{y}{4}=2\Rightarrow y=8\)
\(A=\frac{2}{3}+\frac{3}{4}\left(\frac{-4}{9}\right)\)
\(A=\frac{2}{3}+\frac{-1}{3}\)
\(A=\frac{1}{3}\)
\(B=\frac{2}{5}+\frac{3}{5}\div\left(-2\right)\)
\(B=\frac{2}{5}+\frac{-3}{10}\)
\(B=\frac{1}{10}\)
\(C=2\frac{3}{11}\cdot1\frac{1}{12}\cdot\left(-2,2\right)\)
\(C=\frac{325}{132}\cdot\left(-2,2\right)\)
\(C=\frac{-65}{12}\)
\(D=\left(\frac{3}{4}-0,2\right)\left(0,4-\frac{4}{5}\right)\)
\(D=\frac{11}{20}\cdot\frac{-2}{5}\)
\(D=\frac{-11}{50}\)
\(\frac{a}{b}=\frac{3}{5};\frac{b}{c}=\frac{4}{7}\)
\(=>\frac{a}{b}=\frac{12}{20};\frac{b}{c}=\frac{20}{35}\)
\(=>\frac{a}{12}=\frac{b}{20};\frac{b}{20}=\frac{c}{35}\)
\(=>\frac{a}{12}=\frac{b}{20}=\frac{c}{35}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ....
Tự làm nốt nhé :v
\(\frac{a}{b}=\frac{3}{5}\Rightarrow\frac{a}{3}=\frac{b}{5}\Rightarrow\frac{a}{12}=\frac{b}{20}\)
\(\frac{b}{c}=\frac{4}{7}\Rightarrow\frac{b}{4}=\frac{c}{7}\Rightarrow\frac{b}{20}=\frac{c}{35}\)
\(\Rightarrow\frac{a}{12}=\frac{b}{20}=\frac{c}{35}\)
den day tu ap dung
a) \(\frac{a-1}{2}=\frac{b+2}{3}=\frac{c-3}{4}=k\)
\(\Rightarrow\hept{\begin{cases}a=2k+1\\b=3k-2\\c=4k+3\end{cases}}\)thay vào \(3a-2b+c=-46\)
\(\Rightarrow3\left(2k+1\right)-2\left(3k-2\right)+4k+3=-46\)
\(\Leftrightarrow6k+3-\left(6k-4\right)+4k+3=-46\)
\(\Leftrightarrow4k+10=-46\Rightarrow4k=-56\Rightarrow k=-14\)
\(\Rightarrow\hept{\begin{cases}a=2.\left(-14\right)+1=-27\\b=3.\left(-14\right)-2=-44\\c=4.\left(-14\right)+3=-53\end{cases}}\)
Vậy \(a=-27;b=-44;c=-53\)
b) \(\frac{a}{2}=\frac{b}{5}\Rightarrow\frac{a}{6}=\frac{b}{15}\left(1\right)\)
\(\frac{b}{3}=\frac{c}{4}\Rightarrow\frac{b}{15}=\frac{c}{20}\left(2\right)\)
Từ (1) và (2) \(\Rightarrow\frac{a}{6}=\frac{b}{15}=\frac{c}{20}\)
\(\Rightarrow\frac{a}{6}=\frac{b}{15}=\frac{c}{20}=\frac{a+b-c}{6+15-20}=\frac{12}{1}=12\)
\(\Rightarrow\hept{\begin{cases}a=12.6=72\\b=12.15=180\\c=12.20=240\end{cases}}\)
Vậy \(a=72;b=180;c=240\)
a, \(\frac{a-1}{2}=\frac{b+2}{3}=\frac{c-3}{4}\)
\(\Rightarrow\frac{3a-3}{6}=\frac{2b+4}{6}=\frac{c-3}{4}=\frac{3a-3-2b-4+c-3}{6-6+4}=\frac{\left(3a-2b+c\right)-\left(3+4+3\right)}{4}=\frac{-46-10}{4}=-14\)
=> \(\hept{\begin{cases}\frac{a-1}{2}=-14\\\frac{b+2}{3}=-14\\\frac{c-3}{4}=-14\end{cases}}\Rightarrow\hept{\begin{cases}a=-27\\b=-44\\c=-53\end{cases}}\)
b) \(\hept{\begin{cases}\frac{a}{2}=\frac{b}{5}\Rightarrow\frac{a}{6}=\frac{b}{15}\\\frac{b}{3}=\frac{c}{4}\Rightarrow\frac{b}{15}=\frac{c}{20}\end{cases}\Rightarrow\frac{a}{6}=\frac{b}{15}=\frac{c}{20}}=\frac{a+b-c}{6+15-20}=\frac{12}{1}=12\)
=> a = 72, b=180, c=240
a) Ta có: \(\frac{a}{3}=\frac{b}{4}.\)
=> \(\frac{a}{3}=\frac{b}{4}\) và \(a.b=48.\)
Đặt \(\frac{a}{3}=\frac{b}{4}=k\Rightarrow\left\{{}\begin{matrix}a=3k\\b=4k\end{matrix}\right.\)
Có: \(a.b=48\)
=> \(3k.4k=48\)
=> \(12k^2=48\)
=> \(k^2=48:12\)
=> \(k^2=4\)
=> \(k=\pm2.\)
TH1: \(k=2.\)
\(\Rightarrow\left\{{}\begin{matrix}a=2.3=6\\b=2.4=8\end{matrix}\right.\)
TH2: \(k=-2.\)
\(\Rightarrow\left\{{}\begin{matrix}a=\left(-2\right).3=-6\\b=\left(-2\right).4=-8\end{matrix}\right.\)
Vậy \(\left(a;b\right)=\left(6;8\right),\left(-6;-8\right).\)
Chúc bạn học tốt!
\(\frac{a}{5}=\frac{b}{4}\\ \Rightarrow\frac{a^2}{25}=\frac{b^2}{16}=\frac{a^2-b^2}{25-16}=\frac{1}{9}\\ \Rightarrow a^2=\frac{25}{9}\\ \Rightarrow a=\frac{5}{3}\)
tự tính b nhé
b) Câu b tương tự câu a .
Nếu ko biết hỏi mình
Giải:
Ta có: a:b=9:4⇒a9=b4⇒a45=b20
b:c=5:3⇒b5=c3⇒b20=c12
⇒a45=b20=c12
Đặt a45=b20=c12=k⇒a=45kb=20kc=12k
Lại có: a−bb−c=45k−20k20k−12k=(45−20)k(20−12)k=258
Vậy a−bb−c=258
Ta có \(a+b=\frac{5}{2};b+c=\frac{9}{4};c+a=-\frac{5}{4}\)
\(\Rightarrow a+b+b+c+c+a=\frac{5}{2}+\frac{9}{4}+\frac{-5}{4}=\frac{7}{2}\)
\(\Rightarrow2\left(a+b+c\right)=\frac{7}{2}\)
\(\Rightarrow a+b+c=\frac{7}{4}\)
Vậy \(a=\frac{7}{4}-\frac{5}{2}=-\frac{3}{4}\)
\(b=\frac{7}{4}-\frac{9}{4}=-\frac{1}{2}\)
\(c=\frac{7}{4}-\frac{-5}{4}=\frac{12}{4}=3.\)
\(\Rightarrow2\left(a+b+c\right)=\frac{5}{2}+\frac{9}{4}-\frac{5}{4}=\frac{7}{2}\)
Lại có \(2\left(a+b\right)=5\)
\(\Rightarrow2c=\frac{7}{2}-5=\frac{-3}{2}\Rightarrow c=\frac{-3}{4}\)
\(\Rightarrow a=\frac{-5}{4}-\frac{-3}{4}=\frac{-1}{2}\)
\(\Rightarrow b=\frac{5}{2}+\frac{1}{2}=3\)