Question
If x² - 2x + 1 = 0, then find the value of (x⁴ +
x⁻⁴)(x + x⁻¹).Solution
x² - 2x + 1 = 0
x² + 1 = 2x
By dividing both side by 'x' we get,
(x + 1/x) = 2
So, x = 1 [Since we know if (x + 1/x) = 2, then the value of 'x' is 1]
Now, (x⁴ + x⁻⁴)(x + x⁻¹) = (1 + 1)(1 + 1) = 2 × 2 = 4
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