aniido3alyna
aniido3alyna aniido3alyna
  • 13-10-2016
  • Mathematics
contestada

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

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HomertheGenius
HomertheGenius HomertheGenius
  • 21-10-2016
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.
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