ω என்பது ஒன்றின் கன படிமூலமாக இருந்தால், எனில்,    என்ற சமன்பாட்டின் படிமூலம் என்பது

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BPSC Asstt. Prof. ME Held on Nov 2015 (Advt. 22/2014)
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  1. x = ω
  2. x = 0
  3. x = 1
  4. x = ω2

Answer (Detailed Solution Below)

Option 2 : x = 0

Detailed Solution

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கருத்து:

ω என்பது ஒன்றின் கன படிமூலமாக இருந்தால் அதாவது ω3 = 1

பின்னர் 1 + ω + ω2 = 0.

ω4 = ω3ω = ω [∵ ω3 =1]

கணக்கீடு:

கொடுக்கப்பட்டது:

C'1 = C1 + C2

R'2 = R2 - R1 and R'3 = R3 - R1

முதல் நெடுவரிசையுடன் விரிவாக்க:

∴ x[(x + ω2 - ω)(x + ω - ω2) - (1 - ω)(1 - ω2)]

∴ x[x2 + ωx - ω2x + ω2x + ω3 - ω4 - ωx - ω2 + ω3 - 1 + ω2 + ω - ω3]

∴ x3 = 0      (∵ ω3 = 1 and ω4 = ω3ω ⇒ ω)

∴ x = 0.

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