Adding the square of consecutive even numbers gives 8 times the smaller number. What are the 2 even numbers?

Expert Answers
mlsiasebs eNotes educator| Certified Educator

Since we have two unknowns, we need to write two equations to be able to write two equations to solve for them.

We can designate x and y as our two unknown values.  The problem tells us that we have two consecutive even numbers.  Since they are even numbers, they must differ by a value of 2.  Let's assign x as the lesser of the two values and y as the greater value such that

x + 2 = y        This meets the requirement that they be consecutive even numbers.

Now, let's look at how we can set up the second formula to solve for our unknowns.

From the question "Adding the square of consecutive even numbers gives 8 times the smaller number.", we can write our second equation

x^2 + y^2 = 8x

Now, we need to substitute in for y so that we have one equation all in terms of x

x^2 + (x + 2)^2 = 8x

Once we have this point, we need to work out the algebra to simplify this equation.

x^2 + x^2 + 4x + 4 = 8x

2x^2 + 4x - 8x + 4 = 0

2x^2 - 4x + 4 =n0

We can simply this further by dividing the entire equation by 2

x^2 - 2x + 2 = 0

We would then need to use the quadratic formula or determine the roots by inspection.  However, there are no real number solutions to this particular quadratic equation.  I would encourage you to check your problem and/or with your teacher to see if there was an error in the original question.