Question

The sum of 2 numbers is 16, and the sum of their squares is 146. find the 2 numbers

Answer 1

Explanation:

x + y = 16 (*)

x^2 + y^2 = 146 (**)

(*) <=> x= 16-y

substitute x = 16 - y

(**) <=> (16-y)^2 + y^2 = 146

<=> y^2 - 2.16.y + 16^2 + y^2 = 146

<=> 2y^2 - 32y + 110 = 0

<=> y^2 - 16y + 55 = 0

<=> (y-11)(y-5) = 0

<=> y=11 or y= 5

For y = 11, we have x= 16-11=5

For y=5, we have x= 16-5=11

Answer: (x,y) = (11,5) ; (5,11)