If the average of x+1/x be 1 then the value of x^10 +1/x^100 is
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Given : average of x+1/x be 1
To Find : value of x^10 +1/x^100
Solution:
Average of x + 1/x = 1
=> (x + 1/x) /2 = 1
=> (x + 1/x) = 2
=> x² + 1 = 2x
=> x² - 2x + 1 = 0
=> (x - 1)² = 0
=> x = 1
x¹⁰ + 1/x¹⁰⁰ = 1¹⁰ + 1/1¹⁰⁰ = 1 + 1 = 2
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