The differnce of two numbers is 2 the difference of their squares is 20 find the numbers

4 and 6

6-4=2

6^2-4^2
36-16=20

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To find the numbers, let's assign them variables. Let's call the first number "x" and the second number "y".

According to the problem, the difference between the two numbers is 2, which can be written as:

x - y = 2 ...(Equation 1)

The difference of their squares is 20, which can be expressed as:

x^2 - y^2 = 20 ...(Equation 2)

Now, we can solve this system of equations to find the values of x and y.

We can start by rearranging Equation 1 to solve for x in terms of y:

x = y + 2

Now, substitute this value of x in Equation 2:

(y + 2)^2 - y^2 = 20

Expanding the square, we get:

y^2 + 4y + 4 - y^2 = 20

Combining like terms, we have:

4y + 4 = 20

Subtracting 4 from both sides of the equation, we get:

4y = 16

Dividing both sides by 4, we find:

y = 4

Now, substitute this value of y back into x = y + 2:

x = 4 + 2 = 6

Therefore, the numbers are x = 6 and y = 4.