if x and y are positive and x+y=10. Find the minimum value of 1/x + 1/y

Answer 1

Due to symmetry, a shortcut is to set y=x.

x+y=10 becomes x+x=10, 2x=10, x=5.

z = 1/x+1/y = 1/x+1/x = 2/x.

For x=5, 2/x = 2/5 = 0.4

So, x=5, y=5, z=2/5

Answer 2

I took the first equation and solved it for y.

y=10-x

Then I substituted it into the second equation.

1/x+1/(10-x)

I graphed in on the graphing calculator and found the min as (5,0.4)