bạn giải đi bạn

Theo đề ta có: \(x:y:z=3:4:5\Rightarrow\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\)

Đặt: \(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}=k\left(k\inℕ^∗\right)\)

Suy ra: \(x=3k;y=4k;z=5k\) Thay vào biểu thức P ta có:

\(P=\frac{3k+8k+15k}{6k+12k+20k}+\frac{6k+12k+20k}{9k+16k+25k}+\frac{9k+16k+25k}{12k+20k+30k}\)

\(P=\frac{26k}{38k}+\frac{38k}{50k}+\frac{50k}{62k}=\frac{13}{19}+\frac{19}{25}+\frac{25}{31}=\frac{33141}{14725}\)

Ta có \(\frac{x}{5}=\frac{y}{4}=\frac{z}{3}\)

Đặt \(\frac{x}{5}=\frac{y}{4}=\frac{z}{3}=k\Rightarrow\hept{\begin{cases}x=5k\\y=4k\\z=3k\end{cases}}\)

Khi đó P = \(\frac{x+2y-3z}{x-2y+3z}=\frac{5k+2.4k-3.3k}{5k-2.4k+3.3k}=\frac{5k+8k-9k}{5k-8k+9k}=\frac{4k}{6k}=\frac{2}{3}\)

Theo bài ra, ta có :

x:y:z=5:4:3 ⇒x/5=y/4=z/5⇒

Đặt x/5=y/4=z/3=kx5=y4=z3=k ⇒x=5k

y=4k

z=3k⇒x=5ky=4kz=3k

⇒P=x+2y−3z/x−2y+3z=5k+8k−9k/5k−8k+9k=4k/6k=23

Vậy P=23

Ta có x,y,z tỉ lệ với 5,4,3

=> \(\frac{x}{5}\)=\(\frac{y}{4}\)=\(\frac{z}{3}\)

=> x=5.k , y=4.k , z=3.k

=> y =\(\frac{x+2y-3z}{x-2y+3z}\)= \(\frac{5k+2.\left(4k\right)-3.\left(3k\right)}{5k-2.\left(4k\right)+3.\left(3k\right)}\)= \(\frac{5k+8k-9k}{5k-8k+9k}\)= \(\frac{4k}{6k}\)= \(\frac{2}{3}\)

vậy y = \(\frac{2}{3}\)

y=2/3 đúng đo bạn

x; y; z tỉ lệ với 5; 4; 3 

\(\Rightarrow\frac{x}{5}=\frac{y}{4}=\frac{z}{3}\)

\(\Rightarrow\frac{x}{5}=\frac{2y}{8}=\frac{3z}{9}\)

\(\Rightarrow\frac{x+2y-3z}{5+8-9}=\frac{x-2y+3z}{5-8+9}=\frac{x}{5}=\frac{y}{4}=\frac{z}{3}\)

\(\Rightarrow\frac{x+2y-3z}{4}=\frac{x-2y+3z}{6}\)

\(\Rightarrow\frac{x+2y-3z}{x-2y+3z}=\frac{4}{6}=\frac{2}{3}\)