Free help with homework

Why join Brainly?

  • ask questions about your assignment
  • get answers with explanations
  • find similar questions


Xy = 64

the best choice for the answer is...
8*8 = 64

8+8 = 16 
0 0 0
i am sry this is too level for my grade anyway thanku
The Brainliest Answer!
Let the two positive numbers be x and y.
xy = 64
⇒ y = 64/x

Sum, s = x+y = x + (64/x)
now, we have to minimise s.
For s to be minimum, two condition should be satisfied:
1.  \frac{ds}{dx}=0\\2.  \frac{d^2s}{dx^2}\ \textgreater \ 0

 \frac{ds}{dx}= 0 \\ \\ \Rightarrow \frac{d}{dx}(x+ \frac{64}{x}) =0\\\\\Rightarrow1- \frac{64}{x^2}  =0\\\\\Rightarrow \frac{64}{x^2}  =1\\\\\Rightarrow  x^{2} =64\\\\\Rightarrow x= \sqrt{64}=8

Now for second condition,
 \frac{d^2s}{dx^2}= \frac{d^2(x+ \frac{64}{x})}{dx} = \frac{d}{dx}(1- \frac{64}{x^2})  =\frac{2 \times 64}{x^3}

at\ x=8,\\ \\ \frac{2 \times 64}{x^3}=\frac{2 \times 64}{8^3}= \frac{1}{4}\ \textgreater \ 0

So, at x=8, the sum is minimum.
y = 64/8 = 8
So the numbers are (8,8)

1 5 1
thanku again can know what r u currently i mean whether studying or job
thanks boss anyway
you are welcome!:)
The Brain
  • The Brain
  • Helper
Not sure about the answer?
Learn more with Brainly!
Having trouble with your homework?
Get free help!
  • 80% of questions are answered in under 10 minutes
  • Answers come with explanations, so that you can learn
  • Answer quality is ensured by our experts