Question

[Nguyễn Gia Huy]

Tìm a, b, c biết:

a) \(\frac{a-1}{2}=\frac{b+2}{3}=\frac{c-3}{4}=k\)\(\)\(k\)

và \(3a-2b+c=-46\)

b) \(\frac{a}{2}=\frac{b}{5};\frac{b}{3}=\frac{c}{4}\)

và \(a+b-c=12\)

Answer 1

[Nguyễn Tất Đạt]

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 \(a=72;b=180;c=240\)

Answer 2

[ST]

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