Georgia State University
Cynthia R. Algebra 8 months, 2 weeks ago Let the two positive numbers be ‘x’ and ‘y’ Given product is 20 ⇒ xy = 20 ⇒ y = `20/x` Sum S = x + y S = `x + 20/x` `"dS"/("d"x) = 1 - 20/x^2` For maximum or minimum, `"dS"/("d"x)` = 0 x2 – 20 = 0 x2 = 20 x = `+ 2sqrt(5)` x = `- 2sqrt(5)` is not possible `("d"^2"S")/("d"x^2) = 40/x^3` At x = `2sqrt(5), ("d"^2"S")/("d"x^2) > 0` ∴ Sum ‘S’ is minimum when x = `2sqrt(5)` y = `20/(2sqrt(5)) = 2sqrt(5)` Minimum sum = `2sqrt(5) + 2sqrt(5)` = `4sqrt(5)` |