This looks simple but can't figure it out

Question

5=6

8=15

4=9

3=?

Answer 1

I'm not sure what this question is asking, but I'll give it my best shot.

Obviously your equals signs are not really meant to imply equality, so I'll assume these are inputs and outputs of an equation. Please correct me if that is not accurate.

If the numbers on the left are you 'X' values and the numbers on the right are your 'Y' values... Because we can see that these three points do not form a straight line, we will fit them to a quadratic equation so solve for Y(3). Of course, an infinite number of equations will fit this set of points, so this is strictly an exercise based on the assumption that this "question" is a lesson in quadratics.

We can start by breaking this into 3 equations with 3 unknowns (A,B,and C of the quadratic equation). Our points are (4,9), (5,6), and (8,15). Plugging these into the Ax² + Bx + C form gives us:

16*A + 4*B + C = 9

25*A + 5*B + C = 6

64*A + 8*B + C = 15

The quickest way to solve this is through matrices. We first make a matrix from our equations:

16 4 1

25 5 1

64 8 1

We then invert it (You can look up tutorials on how to invert matrices, It would take too long to write out here):

1/4 -1/3 1/12

-13/4 4 -3/4

10 -32/3 5/3

and multiply it by the matrix of our Y values:

9

6

15

The result of this multiplication is:

1/4 * 9 + -1/3 * 6 + 1/12 * 15 = 1.5

-13/4 * 9 + 4*6 + -3/4*15 = -16.5

10*9 + -32/3 * 6 + 5/3 * 15 = 51

So, if we use A=1.5, B=-16.5, and C=51, we get:

Y = 1.5x² - 16.5x + 51

When we plug in X = 3, we get Y = 15

I know I didn't cover the all of the little details. I'd be happy to go through it with you in more detial if you'd like. For now, I hope this helps.

Answer 2

Hi Boris W.,

I can't figure it out either; usually these "riddles" have some off-beat meaning in terms of numbers of letters in the names for the numbers in some language(s) or other, or in references to famous texts (Sonnets of Shakespeare, Psalms, Constitutional Amendments, Commandments, etc.), or other non-mathematical references. If it is pairs of (x, f(x)) terms, then there's an infinite number of possible functions that can fit three Cartesian point pairs, hence an infinite number of possible answers!

-- Cheers, --Mr. d.