the second number is the reciprocal of the fist and the sm is a minimum.

Question

this is my my work and i got stuck

x=first number
y=second number
so y=1/x

then what. i know the answer is 1 and 1.

also can you explain why the answer is 1 and 1 and not just one. it kind oes that to other problems too. like the answers to one of the problems was 55 and 55

by the way the opic is optimization problems

sum not sm

Ok, y= 1/x

xy= 1
sum= x + 1/x

take the derivative..
0= 1 -1 x^-2
x= sqrt 1 = 1
so y= 1
the min occurs at (x,y) of (1,1)
The 1 and 1 means x,y.

You have y(x) = x + 1/x
y'(x) = 1 -1/x²
Setting y' to 0 and solving you should get
-1/x² = 1 or
x² = 1
So x = +/-1
If you require the answer to be positive integers then the answer occurs at x=1, otherwise you'd need to look at the 3rd quadrant and there's no minimum there.
As to why you book lists both numbers, stating x=1 should be sufficient, but I think the authors are giving both numbers for completeness.