what is a sum of two numbers that has product 14 and a diffference of 10

Question

i need help with this for my homework

Answer 1

so we are looking for 2 numbers (x and y) that do the following:

xy=14, x-y=10

So lets solve for one of these variables and then plug into the other equation:

x=10+y ---> (10+y)y=14, 10y+y²=14, y²+10y-14=0, solve for y, y=(-10±sqrt(100-4(1)(-14)))/2

y=1.245 or y= -11.245

we will take the positive number and plug in to solve for x:

x=1.245+10=11.245

so now we solve for the sum:

1.245+11.245=12.49