Question

The difference between two numbers is 9 and the product of the number is 162. Find the numbers

Answer 1

If you make the two numbers X and Y then we can make a system of equations:

Y - X = 9
X*Y = 162

Using the first equation you can set Y equal to (9 + X) and then plug that in to the second equation

X*(9 + X) = 162

Then if we multiply that out and subtract 162 from both sides we get a quadratic equation

X^2 + 9X - 162 = 0

From here you can just factor to get:

(X + 18)(X - 9) = 0
X = -18, 9

Then when you solve for Y you’re two numbers are either (-18, -9) or (9, 18).

Answer 2

This is the answer....

x-y=9

xy=162

x=9+y

(9+y)y=162

y^2+9y-162=0

(y+18)(y-9)=0

y=-18, 9

x-9=9

x+18=9

x=18, -9

y=-18, 9

Hope it helps...