What is its value?

Question

The cube less the square of a number is twice the number. If x is a positive integer, what's its value?

Answer 1

Hi, Anna!

 

I take this question to read:

 

"The cube [of a number] less the square of the [same] number is twice the number."

 

From here, we need to convert this english sentence into a math sentence.  Here are the key elements in the sentence:

"a number" - pick a variable, I like x

"cube" - x³

"less" - subtraction (since this is just "less" and not "less than", we don't need to change the order of the terms)

"square" - x²

"is" - equals

"twice the number" - 2x

 

Now we just assemble everything in the right order and solve for x:

x³ - x² = 2x

x³ - x² - 2x = 0

x (x² - x - 2) = 0

x (x-2) (x+1) = 0

x = 0, 2, and -1

 

The remainder of the question tells us that x is a positive integer, which allows us to eliminate 0 and -1 as possible solutions.  So the number is 2.

 

Hope this helps!

 

Patty