# The sum of 2 numbers is 22 and the sum of their squares is 404. What are the two numbers.

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Let the numbers to be determined be X and Y. Their sum is X + Y = 22 and the sum of their squares is X^2 + Y^2 = 404.

X + Y = 22

=> X = (22 - Y)

Substitute this in X^2 + Y^2 = 404

=> (22 - Y)^2 + Y^2 = 404

=> 484 + Y^2 - 44Y + Y^2 = 404

=> 2Y^2 - 44Y + 80 = 0

=> Y^2 - 22Y + 40 = 0

=> Y^2 - 2Y - 20Y + 40 = 0

=> Y(Y - 2) - 20(Y - 2) = 0

=> (Y - 20)(Y - 2) = 0

Y = 20 gives X = 2

The two numbers are 20 and 2

lenahong114 | High School Teacher | (Level 2) eNoter

Posted on

Sorry, I solved the answer above for 244, my computer displayed the question incorrectly, sorry about that.

lenahong114 | High School Teacher | (Level 2) eNoter

Posted on

If x represent one of the numbers,

the other then is (22-x)

x^2 + (22-x)^2 = 244

solving for x

x^2 + 484 -44x + x^2 = 244

2x^2 -44x + 240 = 0

factoring

(2x - 20)(x -12)= 0

(2x - 20)= 0

x = 10

(x -12)= 0

x = 12

The numbers are 10 and 12