• # question_answer 62) If $a,\,\,\,b,\,\,\,c,\,\,\,d$ and $p$ are distinct non zero real numbers such that $({{a}^{2}}+{{b}^{2}}+{{c}^{2}}){{p}^{2}}$$-2(ab+bc+cd)p+({{b}^{2}}+{{c}^{2}}+{{d}^{2}})\le 0$ then$a,\,\,\,b,\,\,\,c,\,\,\,d$are in A) $A.P.$                        B) $GP$.C) $H.P.$           D)  satisfy$ab=cd$

$({{a}^{2}}+{{b}^{2}}+{{c}^{2}}){{p}^{2}}-2(ab+bc+cd)p$$+{{b}^{2}}+{{c}^{2}}+{{d}^{2}}\le 0$ $\Rightarrow$$({{a}^{2}}{{p}^{2}}-abp+{{b}^{2}})+({{b}^{2}}{{p}^{2}}-2bcp+{{c}^{2}})$ $\Rightarrow$$ap-b=0,\,\,bp-c=0\And cp-d=0$ $\Rightarrow$$\frac{b}{a}=\frac{c}{b}=\frac{d}{c}\Rightarrow a,\,\,b,\,\,c$and$d$in$GP$ Also$ad=be$