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