If a, b, c, d and p are different real numbers such that : (a2+b2+c2)p

1.	If a, b, c, d and p are different real numbers such that : (a2+b2+c2)p2−2(ab+bc+cd)p+(b2+c2+d2)≤0, then show that a, b, c and d are in G.P.
Answer» If a, b, c, d and p are different real numbers such that : $(a^{2} + b^{2} + c^{2}) p^{2} - 2 (a b + b c + c d) p + (b^{2} + c^{2} + d^{2}) \leq 0$ , then show that a, b, c and d are in G.P.

If a, b, c, d and p are different real numbers such that : (a2+b2+c2)p2−2(ab+bc+cd)p+(b2+c2+d2)≤0, then show that a, b, c and d are in G.P.

Answer»

If a, b, c, d and p are different real numbers such that :

$(a^{2} + b^{2} + c^{2}) p^{2} - 2 (a b + b c + c d) p + (b^{2} + c^{2} + d^{2}) \leq 0$ , then show that a, b, c and d are in G.P.