DeterminantHard
Question
The determinant 
= 0, If
= 0, IfOptions
A.x, y, z are in AP
B.x, y, z are in GP
C.x, y, z are in HP
D.xy, yz, zx are in AP
Solution
Given, = 0
Applying C1 → C1 - (pC2 + C3)
⇒
⇒ - (xp2 + yp + yp + z) (xz + y2) = 0
∴ Either xp2 + 2yp + z = 0 or y2 = 0
⇒ x, y, z are in GP.
= 0 Applying C1 → C1 - (pC2 + C3)
⇒
⇒ - (xp2 + yp + yp + z) (xz + y2) = 0
∴ Either xp2 + 2yp + z = 0 or y2 = 0
⇒ x, y, z are in GP.
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