Question

the difference of two positive whole numbers is 3 and the sum of the squares is 117;by calculating,let us write the two numbers?

Answer 1

let 2 numbers be a and b
[tex]a - b = 3 \\ a^2+b^2 =117 \\ (a-b)^2 =a^2+b^2 - 2ab \\ 3^2 = 117 - 2ab \\ ab = \frac{(117 - 9)}{2} = 54 \\ a + b = \sqrt{a^2+b^2+2ab} = \sqrt{117+108} = \sqrt{225} = 15 [/tex]
$2a = (a+b) + (a-b) = 15 + 3 = 18 \\ a = 9 \\ b = a - 3 = 6$