Let the numbers be x and y
According to question-
xy=64⇒y=x64 −(1)
Also Let S be their sum-
S=x+yS=x+x64
Differentiate w.r.t. x-
dxdS=1−x264
Putting dxdS=0⇒1−x264=0⇒x2=64⇒x=±8
Again differentiating dxdS w.r.t. x−
dx2d2S=x3128
dx2d2S at x=8=83128=2
So dx2d2S>0
SO, S is miniumum at x=8
Then Other number y=864=8
Hence The two numbers are 8 and 8.
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