Question

Find two real numbers whose sum is 18 and whose product is a minimum.

Answer 1

this belongs to calculus ?

Answer 2

no. advanced algebra.

Answer 3

x + y = 18
y = 18 - x

Answer 4

etc.etc.etc...

Answer 5

so can you now find the function to minimize only in terms of 'x' or 'y' ?

Answer 6

no. i really dont have any idea.

Answer 7

Hint: Substitute!

Answer 8

f = xy
x+y= 18
so, y =18-x
put this in xy
what do u get ?

Answer 9

x(18-x)

Answer 10

so, f (x) = 18x - x^2
do you know how to minimize this ?

Answer 11

Convert to vertex form, that should make it easy to solve :)

Answer 12

use am<=gm

Answer 13

or use the fact that for \(ax^2+bx+c\)
the miminum value of x is -b/a

Answer 14

Many ways ^.^