High School

The sum of two numbers is 19. The sum of the squares of the numbers is 193. Find the two numbers.

Answer :

x + y = 19

Additionally, we know that the sum of the squares of the two numbers is 193. This can be expressed as:

x^2 + y^2 = 193

To solve these two equations simultaneously, we can use substitution or elimination method.

One possible approach is to square the first equation and subtract it from the second equation, which eliminates the y variable:

(x^2 + 2xy + y^2) - (x + y)^2 = 193 - 19^2

x^2 + y^2 + 2xy - (x^2 + 2xy + y^2) = 193 - 361

-2xy = -168

Dividing both sides by -2 gives us:

xy = 84

Now we have a system of equations:

x + y = 19

xy = 84

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