a) \(\dfrac{12-7x}{-13}=\dfrac{4-3x}{-5}\)
\(\Rightarrow\left(12-7x\right).\left(-5\right)=\left(-13\right).\left(4-3x\right)\)
\(\Leftrightarrow35x-60=39x-52\)
\(\Rightarrow35x-39x=60-52\)
\(\Rightarrow-4x=8\)
\(\Rightarrow x=-2\)
Vậy \(x=-2.\)
b) Giải
Đặt \(\dfrac{x}{5}=\dfrac{y}{7}=k\)
\(\Rightarrow\left\{{}\begin{matrix}x=5k\\y=7k\end{matrix}\right.\)
Mà \(x+y=48\)
\(\Rightarrow5k+7k=48\)
\(\Leftrightarrow12k=48\)
\(\Leftrightarrow k=48:12\)
\(\Leftrightarrow k=4\)
Vậy \(\left\{{}\begin{matrix}x=5k=5.4=20\\y=7k=7.4=28\end{matrix}\right.\).
c) Giải
Đặt \(\dfrac{x}{3}=\dfrac{y}{4}=k\)
\(\Rightarrow\left\{{}\begin{matrix}x=3k\\y=4k\end{matrix}\right.\)
Mà \(x^2+y^2=100\)
\(\Rightarrow\left(3k\right)^2+\left(4k\right)^2=100\)
\(\Leftrightarrow3^2.k^2+4^2.k^2=100\)
\(\Leftrightarrow k^2\left(3^2+4^2\right)=100\)
\(\Leftrightarrow k^2.25=100\)
\(\Rightarrow k^2=4\)
\(\Rightarrow k=\pm2\)
\(\circledast k=2\Rightarrow\left\{{}\begin{matrix}x=3k=3.2=6\\x=4k=4.2=8\end{matrix}\right.\)
\(\circledast k=-2\Rightarrow\left\{{}\begin{matrix}x=3k=3.\left(-2\right)=-6\\y=4k=4.\left(-2\right)=-8\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=6;y=8\\x=-6;y=-8\end{matrix}\right.\).
\(a,\dfrac{12-7x}{-13}=\dfrac{4-3x}{-5}\)
⇒ \(\dfrac{-12+7x}{13}=\dfrac{-4+3x}{5}\)
⇒ \(5.\left(-12+7x\right)=13.\left(-4+3x\right)\)
⇒ \(-60+35x=-52+39x\)
⇒ \(-60+52=39x-35x\)
⇒ \(-8=4x\)
⇒ \(x=-8:4\)
⇒ \(x=-2\)
\(b,\dfrac{x}{5}=\dfrac{y}{7}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có :
\(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{x+y}{5+7}=\dfrac{48}{12}=4\)
⇒ \(\dfrac{x}{5}=4;\dfrac{y}{7}=4\)
⇒ \(x=5.4;y=7.4\)
⇒ \(x=20;y=28\)
\(c,\dfrac{x}{3}=\dfrac{y}{4}\)
⇒ \(\left(\dfrac{x}{3}\right)^2=\left(\dfrac{y}{4}\right)^2=\dfrac{x^2}{3^2}=\dfrac{y^2}{4^2}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có :
\(\dfrac{x^2}{9}=\dfrac{y^2}{16}=\dfrac{x^2+y^2}{9+16}=\dfrac{100}{25}=4\)
⇒\(\dfrac{x^2}{9}=4;\dfrac{y^2}{16}=4\)
⇒ \(x^2=9.4;y^2=16.4\)
⇒ \(x^2=36;y^2=64\)
⇒ \(x=+-6;y=+-8\)
Vì \(\dfrac{x}{3}=\dfrac{y}{4}\) nên x;y cùng dấu
⇒ \(x=6,y=8\)
\(x=-6,y=-8\)
