Question

Tìm x,y,z biết: x/2=y/3 ; y/4=z/5 và x^2 - y^2 = -16

Answer 1

Ta có: +) \(\dfrac{x}{2}=\dfrac{y}{3}=>\dfrac{x}{8}=\dfrac{y}{12}\)

+) \(\dfrac{y}{4}=\dfrac{z}{5}=>\dfrac{y}{12}=\dfrac{z}{15}\)

Từ trên suy ra \(\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}\)

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

\(\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{x^2-y^2}{64-144}=\dfrac{-16}{-80}=\dfrac{1}{5}\)

=> x=\(\dfrac{1}{5}.8=\dfrac{8}{5}\) ; y=\(\dfrac{1}{5}.12=\dfrac{12}{5}\) ; z=\(\dfrac{1}{5}.15=\dfrac{15}{5}=3\)

Vậy x=\(\dfrac{8}{5}\) ; y=\(\dfrac{12}{5}\) ; z=3