Question

If for non-zero x, x² - 4x - 1 = 0, what is the value of x² + 1/x²?

A 4 Correct Answer Incorrect Answer
B 10 Correct Answer Incorrect Answer
C 12 Correct Answer Incorrect Answer
D 18 Correct Answer Incorrect Answer

Solution

Given, x² - 4x - 1 = 0 ⇒ x - 4 - 1/x = 0   [Dividing both sides by x] ⇒ x - 1/x = 4 ⇒ (x - 1/x)² = 4²   [Squaring on both sides] ⇒ x² + 1/x² - 2 = 16 ⇒ x² + 1/x² = 18

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