Question

Cho x/y = y/z = z/t 

CMR x/t = (x+y+z/y+z+t)^3

Answer 1

Đặt x/y=y/z=z/t=k

=>x=yk; y=zk; z=tk

=>x=yk; y=tk^2; z=tk

=>x=tk^3; y=tk^2; z=tk

\(\dfrac{x}{t}=\dfrac{tk^3}{t}=k^3\)

\(\left(\dfrac{x+y+z}{y+z+t}\right)^3=\left(\dfrac{tk^3+tk^2+tk}{tk^2+tk+t}\right)^3=\left(\dfrac{tk\left(k^2+k+1\right)}{t\left(k^2+k+1\right)}\right)^3=k^3\)

=>\(\dfrac{x}{t}=\left(\dfrac{x+y+z}{y+z+t}\right)^3\)

Answer 2