equation, set up a word problem

Question

Set up an equation and solve the following problem.The cube of a number equals sixteen times the same number. Find the number.

 

x=__________  smallest vallue

x=__________

x=___________ largest value

Answer 1

Let x = the number

 

x³ = 16x

 

A trivial solution is x=0, but we will assume a non-trivial solution.

 

Divie by x on both sides and get

 

x² = 16

 

x = ±4

 

If you include the trivial solution, then x = -4, 0, or 4

Answer 2

x³ = 16x

x³ - 16x = 0

x(x² - 16) = 0

x(x + 4)(x - 4) = 0

 

x = 0

 

x + 4 = 0

x = -4

 

x - 4 = 0

x = 4

 

x = -4 (smallest)

x = 0

x = 4 (largest