Question

cho các số dương x,y,z tỉ lệ với 3,4,5. Tính giá trị của biểu thức

\(P=\dfrac{x+2y+3z}{2z+3y+4z}+\dfrac{2z+3y+4z}{3x+4y+5z}+\dfrac{3x+4y+5z}{4x+5y+6z}\)

Answer 1

Xét \(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}=k\)

\(\Rightarrow\left\{{}\begin{matrix}x=3k\\y=4k\\z=5k\end{matrix}\right.\) (1)

Thay (1) vào P

=> P = \(\dfrac{3k+2.4k+3.5k}{2.5k+3.4k+4.5k}+\dfrac{2.5k+3.4k+4.5k}{3.3k+4.4k+5.5k}\) + \(\dfrac{3.3k+4.4k+5.5k}{4.3k+5.4k+6.5k}\)

=> P = \(\dfrac{26k}{42k}+\dfrac{42k}{50k}\) + \(\dfrac{50k}{62k}\)

=> P = \(\dfrac{13}{21}+\dfrac{21}{25}+\dfrac{25}{31}\approx2,265499232\)

Answer 2

lộn đề .

Thay 2z + 3y + 4z = 2x+ 3y + 4z nha