Question

Find two numbers ,when added equal 13 and multiplied equal 420

Answer 1

let the two numbers are x and y
so according to equation
$x + y = 13 \\ y = 13 - x \\ put \: the \: value \: of \: y \: into \: following \: equation \\ xy = 420 \\ x(13 - x) = 420 \\ 13x - {x}^{2} - 420 = 0 \\ - {x}^{2} + 13x - 420 = 0 \\ {x}^{2} - 13x + 420 = 0 \\ factors \: are \: not \: possible \\ apply \: quadratic \: formula \\ check \: discriment \: d = {b}^{2} - 4ac \\ d = {13}^{2} - 4 \times 420 \\ = 169 - 1680 \\ = - 1511 \\ d < 0 \: no \: real \: roots \: are \: exists \\ i \\ that \: is \: no \: such \: numbers \: exists$

Answer 2

Answer:

The number are 15 and 28