Question
Download Solution PDFIf \(K + \frac{1}{K} = 3 \), then what is the value of \({k^2} + \frac{1}{{{k^2}}}\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(K + \frac{1}{K} = 3 \)
Formula used:
(a + b)2 = a2 + 2ab + b2
Calculation:
Let us square both sides:
\((K + \frac{1}{K} )^2\) = 32
k2 + (2 × k × \(1 \over k\)) + \(1 \over k^2\) = 9
k2 + 2+ \(1 \over k^2\) = 9
k2 + \(1 \over k^2\) = 9 - 2
k2 + \(1 \over k^2\) = 7
∴ The value of k2 + \(\bf 1 \over k^2\) is 7.
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