Question

The product of three consecutive integers is -1716. what is the greatest of the three integers?

Answer 1

Answer:

-11

Step-by-step explanation:

If we call x the least integer, then x + 1 is the next integer, and x + 2 is the greatest integer.

x (x + 1) (x + 2) = -1716

x (x² + 3x + 2) = -1716

x³ + 3x² + 2x = -1716

x³ + 3x² + 2x + 1716 = 0

That's not an easy equation to factor.  We could use rational root test, but that would take a long time.  However, we can narrow down the options logically.  The three integers are relatively close together, so if we approximated the product as x³:

x³ ≈ -1716

x ≈ -11.9

So let's see if x = -12 is a solution:

(-12)³ + 3(-12)² + 2(-12) + 1716 = 396

Nope.  Let's try x = -11:

(-11)³ + 3(-11)² + 2(-11) + 1716 = 726

Not that either.  Let's go the other direction, x = -13:

(-13)³ + 3(-13)² + 2(-13) + 1716 = 0

Aha!  x = -13.  So x + 1 = -12, and x + 2 = -11.

-11 × -12 × -13 = -1716

The greatest integer is -11.