Question

Find two numbers with:
a sum of 45 and a product of 296
a sum of 6.1 and a product of 8.58
a sum of 8 and a product of 14.79

Answer 1

Step-by-step explanation:

Let the numbers be x and y

Given

$x + y = 45 \\ xy = 296 \: or \: x = \frac{296}{y}$

Hence we can write

$y + \frac{296}{y} = 45 \\ {y }^{2} + 296 = 45y \\ {y}^{2} - 45y + 296 = 0 \\ {y}^{2} - 37y - 8y + 296 = 0 \\ y(y - 37) - 8(y - 37) = 0 \\ (y - 37)(y - 8) = 0 \\ y = 37 \: or \: y = 8$

hence the numbers are 37 and 8