Question
Download Solution PDFयदि x + \(\frac{1}{x}\) = 1 है, तो x12 + x9 + x6 + x3 + 1 का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
x12 + x9 + x6 + x3 + 1 का मान
if x + (1/x) = 1
x2 + 1 = x
x2 - x + 1 = 0
(x + 1)(x2 - x + 1) = 0 (x + 1)
(x3 + 13) = 0
x3 = -1
प्रयुक्त सूत्र:
x + 1/x = 1 है, तो x3 = -1
गणना:
प्रश्न के अनुसार,
x12 + x9 + x6 + x3 + 1
⇒ (x3)4 + (x3)3 + (x3)2 + (x3) + 1
⇒ (−1)4 + (-1)3 + (-1)2 + (-1) + 1
⇒ 1 - 1 + 1 - 1 + 1
⇒ 3 - 2 = 1
∴ x12 + x9 + x6 + x3 + 1 का मान 1 है।
Last updated on Jun 13, 2025
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