Question

divide 30 into two parts so that the sum of their squares is a minimum

Answer 1

What course is this?

Answer 2

uhm quadratic equations

Answer 3

a+b=30
a^2+b^2=p(a,b)
minimize p basically

Answer 4

well, just logically you know that for example: \(\large\color{red}{ 40^2+1^2>20^2+20^2 }\)

Answer 5

ok ok

Answer 6

this is an optimization problem?
because accroding to what Positron posted it really lokes like one.

Answer 7

it was asked to be solved using quadratic equations

Answer 8

I lost connection. Love this place.
Anyway... I really don't know how to actually solve (without using a pure logic) if I am not taking the derivative of your function when you solve the a^2+b^2=S for one variable.

Like I was thinking of basic calc problem, but not just using a quadratic equation.

Answer 9

haha yeah, I often loose connections too.
they say it would be like x^2+(30-x)^2=0
but I don't understand much of it

Answer 10

and how do they know to set it to zero. i see they are plugging b-30 for a, and re-writing the Bs with Xs.

Answer 11

I don't understand it either. I think it is not the correct way....

Answer 12

Oh, and I remeber that it should be used with the extreme values lik V(h,k)

Answer 13

this is calculus problem

Answer 14

:)

Answer 15

you don't need calculus to do this problem

Answer 16

well consider the two pat are x and y
since x+y=30====> y=x-30
then S=x^2+(x-30)^2

Answer 17

that may be but the problem is asking for calculus here i would guess

Answer 18

or just logic?

Answer 19

Again, it is logical, and makes sens that: \(\large\color{black}{ 25^2+25^2<50^2+1^2~.}\)

Answer 20

\[x^2+(30-x)^2=2x^2-60x+900\]

this is a quadratic that goes up. it has a min at the vertex



\[\frac{-(-60)}{2\cdot 2}=\frac{60}{4}=15\]

Answer 21

hmm yes! quadratic solves the problem too

Answer 22

ty @Zarkon (sorry for tagging)

Answer 23

Oh ok I get it! thanks everyone!