Question

If $a, b, c, d$ and p are distinct real numbers such that$(a² + b² + c²)p² – 2 (ab + bc + cd)p + (b² + c² + d²) = 0$ then is GP

Answer 1

Answer:

Step-by-step explanation:

(a²+b²+c²)p² - (ab+bc+cd)p + (b²+c²+d²) ≤ 0

∴ 2(a²+b²+c²)p² - 2(ab+bc+cd)p + 2(b²+c²+d²) ≤ 0

∴ (a²p² + b² - 2apb ) + ( ... ) + ( ... ) ≤ 0

∴ (ap-b)² + (bp-c)² + (cp-a)² ≤ 0