Question

1,cho các số a,b,c,d thỏa mãn a/3b=b/3c=c/3d=d/3a.cmr a=b=c=d

2,tìm x,y biết x-y/3=x+y/13=xy/200

3,tìm x,y,z biết 15/x-y=20/y-12=40/z-24 và xy=1200

Answer 1

Ta có \(\dfrac{a}{3b}=\dfrac{b}{3c}=\dfrac{c}{3d}=\dfrac{d}{3a}\)

Áp dụng tính chất dãy tỉ số bằng nhau

\(\Rightarrow\dfrac{a}{3b}=\dfrac{b}{3c}=\dfrac{c}{3d}=\dfrac{d}{3a}=\dfrac{a+b+c+d}{3\left(a+b+c+d\right)}=\dfrac{1}{3}\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{3b}=\dfrac{1}{3}\\\dfrac{b}{3c}=\dfrac{1}{3}\\\dfrac{c}{3d}=\dfrac{1}{3}\\\dfrac{d}{3a}=\dfrac{1}{3}\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}3a=3b\\3b=3c\\3c=3d\\3d=3a\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a=b\\b=c\\c=d\\d=a\end{matrix}\right.\)

\(\Leftrightarrow a=b=c=d\) ( đpcm )