câu a) không có k nha! Mik ghi nhầm

u là troi

Độ dài cạnh thứ nhất \(\frac{60}{4+5+6}x4=16\)

Độ dài cạnh thứ hai\(\frac{60}{4+5+6}x5=20\)

Độ dài cạnh thứ ba\(\frac{60}{4+5+6}x6=24\)

\(2^{x-3}-3.2^x=-92\)

\(\Rightarrow2^x:2^3-3.2^x=-92\)

\(\Rightarrow2^x.\frac{1}{2^3}-3.2^x=-92\)

\(\Rightarrow2^x.\left(\frac{1}{2^3}-3\right)=-92\)

\(\Rightarrow2^x.\frac{-23}{8}=-92\)

\(\Rightarrow2^x=2^5\)

\(\Rightarrow x=5\)

\(P=\left(\frac{3}{2}-\frac{2}{5}+\frac{1}{10}\right):\left(\frac{3}{2}-\frac{2}{3}+\frac{1}{12}\right)\)

\(P=\left(\frac{15}{10}-\frac{4}{10}+\frac{1}{10}\right):\left(\frac{18}{12}-\frac{8}{12}+\frac{1}{12}\right)\)

\(P=\frac{12}{10}:\frac{11}{12}\)

\(P=\frac{6}{5}\times\frac{12}{11}\)

\(P=\frac{72}{55}\)

\(P=\left(\frac{3}{2}-\frac{2}{5}+\frac{1}{10}\right):\left(\frac{3}{2}-\frac{2}{3}+\frac{1}{12}\right)\)

\(\Rightarrow P=\frac{\frac{3}{2}-\frac{2}{5}+\frac{1}{10}}{\frac{3}{2}-\frac{2}{3}+\frac{1}{12}}\)\(\Rightarrow P=\frac{\frac{15}{10}-\frac{4}{10}+\frac{1}{10}}{\frac{18}{12}-\frac{8}{12}+\frac{1}{12}}\)

\(\Rightarrow P=\frac{1}{\frac{3}{4}}=\frac{4}{3}\)

Vì \(\hept{\begin{cases}a+b+c\ne0\\\frac{a}{b}=\frac{b}{c}=\frac{c}{a}\end{cases}}\)

Áp dụng tính chất dãy tỉ số bằng nhau , ta có :

\(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}=\frac{a+b+c}{b+c+a}=1\)

\(\Rightarrow\hept{\begin{cases}a=b\\b=c\\c=a\end{cases}}\Rightarrow a=b=c\text{ mà }a = 2012\Rightarrow\hept{\begin{cases}b=2012\\c=2012\end{cases}}\)

\(\frac{5^{100}.9^{1000}}{3^{2000}.25^{50}}\)

\(=\frac{5^{100}.\left(3^2\right)^{1000}}{3^{2000}.\left(5^2\right)^{50}}\)

\(=\frac{5^{100}.3^{2000}}{3^{2000}.5^{100}}\)

\(=1\)

Vì \(\frac{x}{4}=\frac{4}{7}\)\(\Rightarrow x=\frac{4}{7}.4=\frac{16}{7}\)

Mà xy = 12

\(\Rightarrow\frac{16}{7}.y=12\)

\(\Rightarrow y=\frac{21}{4}\)

\(\frac{\left(5.20\right)^4}{\left(25.4\right)^5}\)=\(\frac{100^4}{100^5}\)=\(\frac{1}{100}\)