Hello!
Let's write these sentences as a system, considering the numbers as x and y:
• difference is 11
(x - y) = 11
• product is 432
(x * y) = 432
System:
First, let's isolate the x variable in the first equation:
Now, let's replace where's x in the second equation with this obtained expression:
Let's solve using the distributive property:
Let's find the coefficients a, b and c:
• a = 1
,
• b = 11
,
• c = - 432
Now, let's solve this quadratic equation that we obtained, using the Quadratic Formula:
In this step, as we have + - in the formula we must divide it into two possible values:
As the exercise asks for positive numbers, we found y = 16.
Now, we have to find X too. To obtain it, we just have to replace y with 16 in any of the equations. I'll do it in the first equation, look:
So, the answer will be:
(x, y) = (27, 16).