Sum/Difference of Cubes When solving a sum of cubes or a difference of cubes you will always get one real soloution and 2 complex conjugate solutions. For the two complex solutions, you need to solve the trinomial using the Quadratic Formula. Prove that when using the quadratic formula for the two complex solutions, the radicand in the final answer is always 3 (sqrt3). In addition, prove that the value of the '-b' and the coefficient of the square root is always the same number. HINT: This is an algebraic proof. Use a general example that will apply to all cases. You only need to show it for the sum of cubes or difference of cubes, but not both. (a^3 x^3 - b^3) = (ax-b)(a^2 x^2 + abx + b^2) or (a^3 x^3 + b^3) = (ax+b)(a^2 x^2 - abx + b^2)
- print Print
- list Cite
Expert Answers
Luca B.
| Certified Educator
calendarEducator since 2011
write5,348 answers
starTop subjects are Math, Science, and Business
You need to solve for x the equation`a^3x^3 + b^3 = 0` , hence, you need to convert the sum of cubes into a product such that:
`a^3x^3 + b^3 = (ax + b)(a^2x^2- abx + b^2)`
`a^3x^3 + b^3 = 0 => (ax + b)(a^2x^2 - abx + b^2) = 0`
You need to set the factors of product equal...
(The entire section contains 157 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- Which of the following is a factor of both x^2-x-6 and x^2-5x +6? A. x-3 B. x+3 C. x-2 D x+2
- 1 Educator Answer
- If a and b are positive numbers, prove that the equation a/x^3 + 2x^2 - 1 + b/x^3 + x - 2 =...
- 1 Educator Answer
- If f(x)=x^3-(a+b)x^2 +abx, find the value of f(a). What is the significance of x-a?
- 1 Educator Answer
- The integral of dx/x^2 sqrt(x^2 + 9) from sqrt(3) to cube root of 3Using trigonometric substitution
- 1 Educator Answer
- Which is the value of the sum x1^3 + x2^3 if x1,x2 are solutions of the equation x^2-5x+6=0
- 1 Educator Answer