Let a, b, c, d and p be any non zero distinct real numbers such that ( a^2+ b^2+ c^2) p^2- 2( ab + bc + cd ) p +( b^2+ c^2+ d^2)=0. Then:

Let $\displaystyle \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}$ and p be any non zero distinct real numbers such that $\displaystyle \left(\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2\right) \mathrm{p}^2-$ $\displaystyle 2(\mathrm{ab}+\mathrm{bc}+\mathrm{cd}) \mathrm{p}+\left(\mathrm{b}^2+\mathrm{c}^2+\mathrm{d}^2\right)=0$. Then :