Question
Download Solution PDFIf K + \(\frac{1}{K}\) + 2 = 0 and K < 0, then what is the value of K11 + \(\frac{1}{K^4}\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
K + \(\frac{1}{K}\) + 2 = 0 and K < 0
Concept used:
(a2 + 2ab + b2) = (a + b)2
Calculation:
K + \(\frac{1}{K}\) + 2 = 0
⇒ k2 + 2k + 1 = 0
⇒ (k + 1)2 = 0
⇒ (k + 1) = 0
⇒ k = -1
Now, K11 + \(\frac{1}{K^4}\)
⇒ (-1)11 + \(\frac{1}{(-1)^4}\)
⇒ -1 + 1
⇒ 0
∴ The value of K11 + \(\frac{1}{K^4}\) is 0.
Last updated on Jul 23, 2025
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