Question

Find two numbers which differ by 4 and whose product is 45

Answer 1

The two solutions are

5 and 9

-5 and -9

Explanation:

Let x and y be the numbers

x-y = 4

x*y = 45

Using substitution

x = 4+y

(4+y)y =45

4y + y^2 = 45

Subtract 45 from each side

y^2 +4y -45 =0

Factor

(y - 5) ( y+9) = 0

Using the zero product property

y -5 =0 y+9 =0

y=5 y = -9

Now we can find x

y=5

x = 4+y

x =4+5

x=9

y = -9

x = 4+y

x = 4+-9

x = -5

The two solutions are

5 and 9

-5 and -9