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Basic Mathematics QUESTION #7946
Question 1
If \(\left[x^3 + \dfrac{1}{x^3}\right] = 52\), find the value of \(x + \dfrac{1}{x}\):
  • 4✔️
  • 3
  • 6
  • 13
Correct Answer Explanation
Using the identity: \(\left(x+\dfrac{1}{x}\right)^3 = x^3 + \dfrac{1}{x^3} + 3\left(x+\dfrac{1}{x}\right)\)
Let \(a = x + \dfrac{1}{x}\): \(a^3 - 3a = 52\).
Testing \(a=4\): \(64 - 12 = 52\) ✓
So \(x + \dfrac{1}{x} = 4\).