Question

Find two numbers whose product is -182 and sum is +1.

Answer 1

Answer:

14 and -13

Step-by-step explanation:

$xy = - 182 \\ x = \frac{ - 182}{y} \\ \\ x + y = 1 \\ \frac{ - 182}{y} + y = 1 \\ \frac{ - 182 + {y}^{2} }{y} = 1 \\ - 182 + {y}^{2} = 1y \\ {y}^{2} - 182 - y = 0 \\ {y}^{2} - y - 182 = 0 \\ {y}^{2} - 14y+ 13y - 182 = 0 \\ y(y - 14) + 13(y - 14) = 0 \\ y - 14 = 0 \: \: \: or \: \: \: y + 13 = 0 \\ \boxed{y = \underline{ \underline{ \bf14}} \: \: \: or \: \: \: y = \underline{ \underline{ \bf - 13}}} \\ \\ The \: \: two \: \: numbers \: \: are : \\ {\bf14 } \: \: and \: \: { \bf -13} \\ \\ x + y = 1 \\ 14 + ( - 13) = 1 \\ 14 - 13 = 1 \\ 1 = 1 \\ \\ xy = - 182 \\ 14 \times ( - 13) = 182 \\ - 182 = - 182$