Question : If $p^2+\frac{1}{p^{2}}$ = 47, the value of $p+\frac{1}{p}$ is:
Option 1: 5
Option 2: 6
Option 3: 7
Option 4: 8
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Correct Answer: 7
Solution :
Given: $p^2+\frac{1}{p^{2}}$ = 47
Since $(a + b)^2 = a^2 + b^2 + 2ab$
⇒ $(p+\frac{1}{p})^2 = p^2 +\frac{1}{p^2} + 2 × p × \frac{1}{p}$
⇒ ($p + \frac{1}{p}) = 47 + 2 = 49$
Taking root on both sides,
⇒ $p+\frac{1}{p} = 7$
Hence, the correct answer is 7.
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