Nelson’s Order

Algebra Level pending

Professor X. Ponent, a famous physicist, goes around Cal Poly - Nomial and asks questions to random citizens. Professor X. Ponent finds Nelson, a previous student of his, and asks him the following order.

“I demand for this much money:

$ $\frac{x^{2}-9}{x^{2}+6x+9}$ $\times$ $\frac{x^{3}-27}{x^{2}-6x+9}$ $\times$ $\frac{x^{3}-3x^{2}-9x+27}{x^{2}-6x+9}$ - 7”

Right now, this is an expression with all real numbers except 3 and -3, but Nelson knows that Mr. X has a trick up his sleeve. Nelson randomly decides to give him 0 dollars.

“Good job, you know domain. Now, you must figure out, based on how much money you gave me, what is the least possible value of x?"

0 Professor X. Ponent’s First Initial -2 -1

1 solution

Ved Pradhan
May 28, 2018

Hello! I am the author of this problem and this is my solution to it. I believe it is the quickest way to solve the problem, but if you have a faster way, please write it down!

The question in simpler terms is to solve this equation:

$\frac{x^{2}-9}{x^{2}+6x+9}$ $\times$ $\frac{x^{3}-27}{x^{2}-6x+9}$ $\times$ $\frac{x^{3}-3x^{2}-9x+27}{x^{2}-6x+9}$ - 7 = 0

Next, you factor using formulas and then cancel:

$\frac{(x+3)(x-3)}{(x+3)^{2}}$ $\times$ $\frac{(x-3)(x^{2}+3x+9)}{(x-3)^{2}}$ $\times$ $\frac{(x+3)(x-3)^{2}}{(x-3)^{2}}$ - 7 = 0

After you cancel, you get:

$x^{2}$ +3x+9-7=0

$x^{2}$ +3x+2=0

Now you must factor again:

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

If you use the zero product property:

x+2=0 or x+1=0

x=-2 or x=-1

And since we are looking for the least possible answer, our answer is $\boxed{-2}$ .

Nelson’s Order

1 solution

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