\(\frac{2.\left(x+y\right)}{30}=\frac{5.\left(y+z\right)}{30}=\frac{3\left(x+z\right)}{30}\)
= \(\frac{x+y}{15}=\frac{y+z}{6}=\frac{x+z}{10}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có
\(\frac{x+y}{15}=\frac{y+z}{6}=\frac{x+z}{10}\)=\(\frac{x+z-y-z}{10-6}=\frac{x-y}{4}\)
\(\frac{x+y}{15}=\frac{y+z}{6}=\frac{x+z}{10}\)=\(\frac{x+y-x-z}{15-10}=\frac{y-z}{5}\)
---> dp cm
biết 3(x+y)=2(y+z)=5(z+x) cm z-x\(\text{biết 3(x+y)=2(y+z)=5(z+x) cm \frac{z-x}{5}=\frac{y-2}{4}}\)
Chứng minh rằng nếu x+y+z=1 thì \(x^2+y^2+z^2\ge\frac{1}{3}\)
\(2.\left(x-y\right)=5.\left(y+z\right)=3.\left(x+z\right)\)
CM : \(\frac{x-y}{4}=\frac{y-z}{5}\)
Cho \(\frac{x}{y}\)=\(\frac{y}{z}\)=\(\frac{z}{x}\)
Tính \(\frac{x^3.y^2.z^{1930}}{x^{240}}\)(biết x+y+z khác 0)
Nếu khó nhìn thì : x3.y2.z1930/x240
Tìm x, y , z biết
1. \(\frac{x+5}{3}=\frac{y+4}{4}=\frac{z+3}{5}\)và x+y+z=24
2.\(\frac{x-5}{3}=\frac{y-4}{4}=\frac{z-3}{5}\)và x+y+z=36
tim x,y,z khi
\(\frac{x}{7}=\frac{y}{3}va\)x-24=y
\(\frac{x}{5}=\frac{y}{7}=\frac{z}{2}\)va y-x=48
\(\frac{x}{2}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}\)va x-y- z=28
\(\frac{x}{3}=\frac{y}{5}=\frac{z}{7}\)va 2x+3-z=-14
Tìm x,y,z biết
\(a.\frac{x}{3}=\frac{y}{4};\frac{y}{3}=\frac{z}{5}\) và 2x-3y+z=6
\(b.\frac{2x}{3}=\frac{3y}{4}=\frac{4z}{5}\)và x+y+z=49
\(c.\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-4}{4}\)và 2x+3y-z=50
\(d.\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\)và xyz=810
Bài 1. Tìm ba số x, y, z, t biết:
\(\text{x : y : z : t 2 : 3: 4 : 5 & x+ y +z+ t =4}\)
\(\frac{x}{2}=\frac{y}{3};\frac{y}{5}=\frac{z}{4}\text{& x -y+ z 49}\)
Cần gấp
1) A= \(\frac{\frac{3}{4}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
b) Cho 3 so x,y,z la 3 so khac 0 thoa man dieu kien :
\(\frac{y+z-x}{x}=\frac{z+x-y}{y}=\frac{x+y-z}{z}\)
Hay tinh gia tri bieu thuc:\(B=\left(1+\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\left(1+\frac{z}{x}\right)\)
