What two positive real numbers whose product is 50 have the smallest possible sum?

Question

Mathematics

Santos

3 April, 07:51

What two positive real numbers whose product is 50 have the smallest possible sum?

+1

Answers (1)

Know the Answer?

Carlos Huang · Answer 1

X * y = 50

y = 50 / x

S = x + y = x + 50 / x

S' = 1 - 50 / x²

1 - 50 / x² = 0

50 / x² = 1

x² = 50

x = √ 50 = 5 √2

y = 50 / 5√2 = 5 √2

Answer:

Those numbers are: x = 5√2 and y = 5√2.