The sum of two numbers is 20. What is the least possible (minimum) sum of their squares

Question

myininaya · Answer

The sum of two numbers is 20
Do you know how to write this as a mathematical equation?

anonymous · Answer

Im supposed to solve it using completing the squares method

myininaya · Answer

Right!
So Do you know how to write "the sum of two numbers is 20" as a mathematical equation?

anonymous · Answer

No, sorry :(

myininaya · Answer

Do you know what sum means?

anonymous · Answer

The answer you get when u add two numbers

myininaya · Answer

So "the sum of two numbers is 20" can be written as x+y=20
right?

myininaya · Answer

It didn't say what numbers would give us 20
so I just called them x and y

myininaya · Answer

so first sentence gives us x+y=20
do you see that?

anonymous · Answer

Yes, continue

myininaya · Answer

What is the least possible (minimum) sum of their squares

$$S=x^2+y^2$$
So I'm calling the sum of their squares, S

myininaya · Answer

Now if x+y=20
then solving this for y we get what?

anonymous · Answer

Y=20-x .

anonymous · Answer

x+y=20
x^2+y^2=z
z is the min.
x^2+y^2=z is the equation of a circle, so the min. is x=y
x=10
y=10

myininaya · Answer

plug that into our equation we called S

myininaya · Answer

$$S=x^2+(20-x)^2$$
See I just replace y with 20-x
since you said y=20-x

anonymous · Answer

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