Answer to Q149
What is the value of an integer, if the sum of the integer and its inverse is ⁴⁄₂?
Let the integer be x. So inverse of x is ¹⁄ₓ
:sum of the integer and its inverse is ⁴⁄₂
x + ¹⁄ₓ = ⁴⁄₂
x + ¹⁄ₓ can be rewritten as (x² + 1) ÷ x
(x² + 1) ÷ x = 2
x² + 1 = 2x
x² - 2x + 1 = 0
Using the quadratic formula
x = 2 ÷ 2
x = 1
Answer: 1
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