Find two positive numbers that satisfy the given requirements. -The second numbe

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Answered question

2021-09-20

Find two positive numbers that satisfy the given requirements. -The second number is the reciprocal of the first number and the sum is a minimum.

Answer & Explanation

toroztatG

toroztatG

Skilled2021-09-21Added 98 answers

Lets say the two numbers are x and y, and we want to minimize x+y
The assumption is y=1x. Thus, we should minimize x+y=x+1x
Let's define a function f(x)=x+1x, and find its minimum point.
f(x)=x+1x
f(x)=11x2=0x2=1
x=±1
But we are only allowed to use positive numbers, so
x=1
We found x=1 so y=1x=1
Result: 1 and 1

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