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Expert: Sherry Wallin - 5/15/2011


Question

question 1
Dear Sherry,

I have tried all my best to answer the question in the attachment.
Please help.
Thanks
Aba

Answer
Hi Aba~

The primary way to show anything is unique is to assume there is more than one (usually two) and show a contradiction or show that the only solution is that the two are one and the same.

So...

Assume a and b are both solutions to x^3-3x^2 + 4x -5 => a^3-3a^2+4a-5 = 0 and b^3-3b^3+4b-5 = 0 thus they equal each other:

a^3-3a^2+4a-5 = b^3-3b^3+4b-5 =>

a^3-b^3- 3a^2+ 3b^2 + 4a-4b -5 +5 = 0  =>

(a-b)(a^2+ab+b^2) -3(a^2-b^2)+4(a-b) = 0 =>
(a-b)(a^2+ab+b^2) -3(a-b)(a+b) +4(a-b) = 0 =>
(a-b)(a^2+ab+b^2-3a-3b+4) = 0 =>
a-b = 0 or a^2+ab+b^2-3a-3b+4 = 0 =>
a = b or ...

This shows that the answer is unique because you have shown if there are two answers a and b, that they are the same, i.e.,  a = b

Math Prof

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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