Toán Lớp 7: 40/x-30=20/y-15=28/z-21 và x.y.z=22400, giúp em giải bài này ạ, em cảm ơn thầy cô và các bạn nhiều.
\[\begin{array}{l}\frac{{40}}{{x – 30}} = \frac{{20}}{{y – 15}} = \frac{{28}}{{z – 21}}\\dk:x \ne 30;y \ne 15;z \ne 21\\= > \frac{{x – 30}}{{40}} = \frac{{y – 15}}{{20}} = \frac{{z – 21}}{{28}}\\= > \frac{x}{{40}} – \frac{3}{4} = \frac{y}{{20}} – \frac{3}{4} = \frac{z}{{28}} – \frac{3}{4}\\= > \frac{x}{{40}} = \frac{y}{{20}} = \frac{z}{{28}} = k\\= > x = 40k;y = 20k;z = 28k\\x.y.z = 22400\\= > 40k.20k.28k = 22400\\= > {k^3} = 1\\= > k = 1\\= > \frac{x}{{40}} = 1 = > x = 40\\\frac{y}{{20}} = 1 = > y = 20\\\frac{z}{{28}} = 1 = > z = 28\\vay:(x;y;z) = (40;20;28)\end{array}\] Trả lời
\frac{{40}}{{x – 30}} = \frac{{20}}{{y – 15}} = \frac{{28}}{{z – 21}}\\
dk:x \ne 30;y \ne 15;z \ne 21\\
= > \frac{{x – 30}}{{40}} = \frac{{y – 15}}{{20}} = \frac{{z – 21}}{{28}}\\
= > \frac{x}{{40}} – \frac{3}{4} = \frac{y}{{20}} – \frac{3}{4} = \frac{z}{{28}} – \frac{3}{4}\\
= > \frac{x}{{40}} = \frac{y}{{20}} = \frac{z}{{28}} = k\\
= > x = 40k;y = 20k;z = 28k\\
x.y.z = 22400\\
= > 40k.20k.28k = 22400\\
= > {k^3} = 1\\
= > k = 1\\
= > \frac{x}{{40}} = 1 = > x = 40\\
\frac{y}{{20}} = 1 = > y = 20\\
\frac{z}{{28}} = 1 = > z = 28\\
vay:(x;y;z) = (40;20;28)
\end{array}\]