Question

find one of the two positive integers whose product is 196 and whose sum is a minimum. i got 14

Answer 1

probably the square root right?

Answer 2

yeah \(\sqrt{196}=14\)

Answer 3

yeah thanks :)

Answer 4

is it clear, without calculus, that it has to be the square root?

Answer 5

no

Answer 6

ok you say one number is \(x\) and the other \(y\) and you want to minimize \(x+y\) given that \(xy=196\)

Answer 7

then you probably changed it to \[y=\frac{196}{x}\] and went on to find the minimum of \[f(x)=x+\frac{196}{x}\] using cacl

Answer 8

but i say, no it is not "find the minimum of \(x+y\) given \(xy=196\) it is
find the minimum of \(y+x\) given \(yx=196\)"

Answer 9

you say "you idiot, that is exactly the same question doe" and i say
yeah right, you can't tell \(x\) from \(y\)
one is not more special than the other
so the minimum must occur when they are equ8al because you can't tell them apart

Answer 10

if \(x=y\) and \(xy=196\) then \(x=y=\sqrt{196}\)

Answer 11

ok yeah im pretty sure its 14

Answer 12

it is 14

Answer 13

thank you so much!