Question : If ${k}+\frac{1}{{k}}=3$, then what is the value of ${k}^2+\frac{1}{{k}^2}$?
Option 1: 9
Option 2: 6
Option 3: 7
Option 4: 5
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Answer (1)
20th Jan, 2024
Correct Answer: 7
Solution :
${k}+\frac{1}{{k}}=3$
Squaring on both sides,
⇒ $({k}+\frac{1}{k})^2=3^2$
⇒ ${k^2}+\frac{1}{{k}^2}+2=9$
⇒ ${k^2}+\frac{1}{{k}^2}=7$
Hence, the correct answer is 7.
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