SOLUTION: Hello, I stumbled on a Algebra problem in my Algebra Problem book today. The problem is: Joe thought of two numbers, their sum was 20 and the sum of their squares was 300. Wha

Question 365171: Hello, I stumbled on a Algebra problem in my Algebra Problem book today.
The problem is:
Joe thought of two numbers, their sum was 20 and the sum of their squares was 300. What is their product?
I am guessing you have to find all the sums of 20 first?
But the "sum of their squares is 300" part is confusing me.
Is it the two numbers, squared, and the squares then added to receive 300?
WOuld the numbers be negative?
Help would be appreciated, these are the kinds of algebra problems I will require to know for the upcoming quiz.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Joe thought of two numbers, their sum was 20 and the sum of their squares was 300. What is their product?
------------
Use x and y
x + y = 20

Sub for y: y = 20-x

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=200 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 17.0710678118655, 2.92893218813452. Here's your graph:

-----------
x = 10 � 5sqrt(2)
--> x = 10 + 5sqrt(2), y = 10 - 5sqrt(2) or vice versa
The product = 100 - 50 = 50

RELATED QUESTIONS
Hello, I found a confusing word problem in my Algebra book today. The word problem... (answered by jim_thompson5910,josmiceli)

I am working on a problem in algebra. The question is: A student opens a literature book (answered by scott8148)

Hello! So I'm having a hard time on this problem. I know it involves some stuff from... (answered by josgarithmetic)

Hello. I am having a hard time understanding Algebra. I am looking for someone to explain (answered by rfer)

hello, i am new to this online help. I really do not know where consecutive... (answered by Alan3354)

Hello, in my algebra riddle book, I found a problem that does not show the answer in the... (answered by stanbon)

I came across a problem today in my Algebra 2 Book that I am not sure how to approach. I... (answered by scott8148)

Hello, tutor!! I'm in Algebra II right now, and we are currently studdying... (answered by benni1013)

Hello. I recently stumbled across your website while trying to figure out one of my... (answered by mananth)