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)lt=0`, then show that a, b, c and d are in G.P.

Explanation

To solve the problem, we need to show that the numbers \( a, b, c, \) and \( d \) are in geometric progression (G.P.) given the inequality:

\[ (a^2 + b^2 + c^2)p^2 - 2(ab + bc + cd)p + (b^2 + c^2 + d^2) \leq 0 \]

### Step 1: Rewrite the expression

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