Question
The average of a number and its reciprocal is 1. What is
the average of its square, cube and fourth power?Solution
Let the number be x So, its reciprocal = 1/x Average = 1 So, total = 1 × 2 = 2 So, x + 1/x = 2 So, x = 1 Now we know any power of 1 is always 1 So, average = (1 + 1 + 1)/3 = 1 ∴ Average is 1
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