Let the number be x and 1/x, Then, x + 1/x = 10/3 ⇒ (x2 + 1)/x = 10/3 ⇒ 3x2 - 10x + 3 = 0 ⇒ 3x2 - 9x - x + 3 = 0 ⇒ 3x(x - 3) -1 (x - 3) = 0 ⇒ (3x - 1) (x - 3) = 0 ∴ x = 1/3, x = 3
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