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:

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

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

\(\Rightarrow4\left(3x+5y\right)=x-2y\Rightarrow12x+20y=x-2y\Rightarrow11x=-22y\Rightarrow\frac{x}{y}=\frac{-22}{11}=-2\)

\(\frac{3x+5y}{x-2y}=\frac{1}{4}\)

\(\Rightarrow x-2y=4\left(3x+5y\right)\)

\(\Rightarrow x-2y=12x+20y\)

\(\Rightarrow12x-x=20y+2y\)

\(\Rightarrow11x=22y\)

\(\Rightarrow x=2y\Leftrightarrow\frac{x}{y}=2\)

\(\frac{3x+5y}{x-2y}=\frac{1}{4}\)

\(\Rightarrow\left(3x+5y\right).4=x-2y\)

\(\Leftrightarrow12x+20y=x-2y\)

\(\Leftrightarrow11x=-22y\)

\(\Leftrightarrow x=-2y\)

\(\Rightarrow\frac{x}{y}=-\frac{2}{1}\)

\(\frac{3x+5y}{x-2y}=\frac{1}{4}\)

\(\Rightarrow\left(3x+5y\right)4=x-2y\)

\(\Rightarrow12x+20y=x-2y\)

\(\Rightarrow12x-x=-2y-20y\)

\(\Rightarrow11x=-22y\)

\(\Rightarrow\frac{x}{y}=\frac{-22}{11}\)

\(\Rightarrow\frac{x}{y}=-2\)

Ta có:

 \(\frac{x^2}{y^2}=\frac{2y}{y^2}=\frac{-2y}{Y}\)

\(\frac{x^2+2y^1}{300}=\frac{x^2+2y^1}{294}\) 

Áp dụng tính chất dãy tỉ số bằng nhau , ta có:

\(\frac{x^2+2y^1}{300}=\frac{x^2+2y}{294}=\frac{x^2+2y^1-x^2-2y^1}{300-294}=\frac{0}{6}=0\) 

\(\Rightarrow x^2+2y=0\) 

\(\Rightarrow x^2=-2y\) 

Ta có:

\(\frac{x^2}{y^2}=\frac{-2y}{y^2}=\frac{-2}{y}\)

Ta có: \(\frac{3x+5y}{x-2y}=\frac{1}{4}\)

<=> ( 3x + 5y ) .4 = x - 2y <=> 12x  + 20y = x - 2y <=> 11x = -22y <=> x = -2y <=> \(\frac{x}{y}=-2\)

bài 1

\(\frac{3x-y}{x+y}=\frac{3}{4}\)

\(\Rightarrow\left(3x-y\right).4=\left(x+y\right)3\)

\(\Rightarrow12x-4y=3x+3y\)

\(\Rightarrow9x=7y\)

\(\Rightarrow\frac{x}{y}=\frac{7}{9}\)

Vậy \(\frac{x}{y}=\frac{7}{9}\)

bài 2

\(\frac{3x+2}{5x+7}=\frac{3x-1}{5x+4}\)

\(\Rightarrow\) \(\left(3x+1\right)\left(5x+4\right)=\left(3x-1\right)\left(5x+7\right)\)

\(\Rightarrow15x^2+12x+10x+8=15x^2+21x-5x-7\)

\(\Rightarrow22x+8=16x-7\)

\(\Rightarrow22x+16x=-7-8\)

\(\Rightarrow6x=-15\)

\(\Rightarrow x=-2,5\)

Vậy x=-2,5

\(\frac{x-3y}{2x+5y}=\frac{4}{5}\)

\(\Rightarrow\left(x-3y\right).5=\left(2x+5y\right).4\)

\(\Rightarrow5x-15y=8x+20y\)

\(\Rightarrow5x-8x=20y+15y\)

\(\Rightarrow-3x=35y\)

\(\Rightarrow\frac{x}{y}=\frac{-35}{3}\)

Vậy \(\frac{x}{y}=\frac{-35}{3}.\)

Chúc bạn học tốt!

\(\frac{5x-2y}{3x+4y}=\frac{3}{4}\Rightarrow\left(5x-2y\right).4-3\left(3x+4y\right)=0\)

\(\Rightarrow20x-8y-9x-12y=0\)

\(\Rightarrow11x-20y=0\)

\(\Rightarrow11x=20y\)

\(\Rightarrow\frac{x}{y}=\frac{20}{11}\)

từ tỉ lệ thức đã cho ta có;

4(5x-2y)=3(3x+4y)

20x-8y=9x+12y

11x-8y=12y

11x=20y

x/y=20/11