SOLUTION: The sum of two numbers is 32. The sum of the squares of the two numbers is 544. Find the numbers. Thank you for your help, <3 Rae

Question 251552: The sum of two numbers is 32. The sum of the squares of the two numbers is 544. Find the numbers.
Thank you for your help,
<3 Rae
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"The sum of two numbers is 32" translates to

"The sum of the squares of the two numbers is 544" means that

Start with the first equation.

Subtract x from both sides.

Move onto the next equation.

Plug in

FOIL

Subtract 544 from both sides.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

If , then or if then .

This means that the two numbers are simply 20 and 12 (in either order).
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