Tham khảo:Câu hỏi của ๖ۣۜY๖ۣۜi๖ۣۜn l o v e - Toán lớp 7 | Học trực tuyến - H
link:https://h.vn/hoi-dap/question/122934.html
ib mik đưa link ạ:<
Ta có : \(\frac{a-20}{52}=\frac{b-15}{39}=\frac{c-5}{13}\)
=> \(\frac{a}{52}-\frac{20}{52}=\frac{b}{39}-\frac{15}{39}=\frac{c}{13}-\frac{5}{13}\)
=> \(\frac{a}{52}-\frac{5}{13}=\frac{b}{39}-\frac{5}{13}=\frac{c}{13}-\frac{5}{13}\)
=> \(\frac{a}{52}=\frac{b}{39}=\frac{c}{13}\)
Đặt \(\frac{a}{52}=\frac{b}{39}=\frac{c}{13}=k\)
=> \(\hept{\begin{cases}a=52k\\b=39k\\c=13k\end{cases}}\)
=> b.c = 39k.13k
=> 507k2 = 3
=> k = \(\pm\frac{1}{13}\)
=> \(\hept{\begin{cases}a=52\cdot\frac{1}{13}=4\\b=39\cdot\frac{1}{13}=3\\c=13\cdot\frac{1}{13}=1\end{cases}}\)hoặc \(\hept{\begin{cases}a=52\cdot\left(-\frac{1}{13}\right)=-4\\b=39\cdot\left(-\frac{1}{13}\right)=-3\\c=13\cdot\left(-\frac{1}{13}\right)=-1\end{cases}}\)
Tại hạ xin test cách khác :))
\(\frac{52}{a-20}=\frac{39}{b-15}=\frac{13}{c-5}\)
\(=>\frac{a-20}{52}=\frac{b-15}{39}=\frac{c-5}{13}\)
\(=>\frac{a}{52}-\frac{5}{13}=\frac{b}{39}-\frac{5}{13}=\frac{c}{13}-\frac{5}{13}\)
\(=>\frac{a}{52}=\frac{b}{39}=\frac{c}{13}\)
\(=>\frac{a^2}{52^2}=\frac{b^2}{39^2}=\frac{c^2}{13^2}=\frac{bc}{39.13}=\frac{3}{13^2.3}=\frac{1}{13^2}\)
\(=>\hept{\begin{cases}\frac{a^2}{52^2}=\frac{1}{13^2}=>a^2=\frac{1}{13^2}.52^2=4^2\\\frac{b^2}{39^2}=\frac{1}{13^2}=>b^2=\frac{1}{13^2}.39^2=3^2\\\frac{c^2}{13^2}=\frac{1}{13^2}=>c^2=\frac{1}{13^2}.13^2=1^2\end{cases}}\)
\(=>\hept{\begin{cases}a=\pm4\\b=\pm3\\c=\pm1\end{cases}}\)
