Question
Download Solution PDFযদি ω একের ঘনমূল হয়, তাহলে নীচের সমীকরণের একটি মূল কত?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFধারণা:
ω যদি একের ঘনমূল হয়, অর্থাৎ ω3 = 1
তাহলে 1 + ω + ω2 = 0
ω4 = ω3ω = ω [∵ ω3 =1]
গণনা:
প্রদত্ত:
C'1 = C1 + C2
R'2 = R2 - R1 এবং R'3 = R3 - R1
প্রথম স্তম্ভকে প্রসারিত করে:
∴ 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 এবং ω4 = ω 3 ω ⇒ ω)
∴ x = 0
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