Can someone check my working on this algebra? (alpha) + (beta) = -5/2, (alpha)(beta) = -5, (alpha)^2 + (beta)^2 = 65/4, (alpha)^3 + (beta)^3 = -425/8
- Thread starter Laia
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Laia, your post does not belong in this subforum. You should have posted it in one such as "Intermediate/Advanced Algebra," for example. Also, your second attachment should have been posted in a separate thread with you possibly giving a link to the first attachment, as it has the conditions on the variables.
The second attachment also needs attention, but I will address part of the first one only.
For convenience, let x = Alpha and let y = Beta. The following is a translation.
In your first attachment, you are correct up to and including your sixth line. However, there is not a common \(\displaystyle \ x^2y^2 \ \) factor available to factor out from every term in the numerator to produce the numerator in the seventh line.
Try these two steps and work further. (Just change the variables into the appropriate Alphas and Betas, respectively.)
\(\displaystyle \dfrac{x^3y^2 + x^2y^3 - (x^2 + y^2)}{x^2y^2} \ = \)
\(\displaystyle \dfrac{x^2y^2(x + y) - (x^2 + y^2)}{x^2y^2} \ = \ ?\)
P.S. I cannot stay around to answer possible follow-up questions for at least the next several hours.
The second attachment also needs attention, but I will address part of the first one only.
For convenience, let x = Alpha and let y = Beta. The following is a translation.
In your first attachment, you are correct up to and including your sixth line. However, there is not a common \(\displaystyle \ x^2y^2 \ \) factor available to factor out from every term in the numerator to produce the numerator in the seventh line.
Try these two steps and work further. (Just change the variables into the appropriate Alphas and Betas, respectively.)
\(\displaystyle \dfrac{x^3y^2 + x^2y^3 - (x^2 + y^2)}{x^2y^2} \ = \)
\(\displaystyle \dfrac{x^2y^2(x + y) - (x^2 + y^2)}{x^2y^2} \ = \ ?\)
P.S. I cannot stay around to answer possible follow-up questions for at least the next several hours.
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Thread moved.
Would it be correct to assume that the first four lines are the "givens", and that the starred line indicates the beginnings of computations based on those givens? So the problem statement was along the lines of the following?
[imath]\qquad \textrm{Given that } \alpha + \beta = -\frac{5}{2},\; \alpha \beta = -5,[/imath]
[imath]\qquad \alpha^2 + \beta^2 = \frac{65}{4}, \textrm{ and } \alpha^3 + \beta^3 = -\frac{425}{8},[/imath]
[imath]\qquad \textrm{find the values of the expressions below: }[/imath]
[imath]\qquad \qquad \textrm{(a) } \left(\alpha - \frac{1}{\alpha^2}\right) + \left(\beta - \frac{1}{\beta^2}\right)[/imath]
[imath]\qquad \qquad \textrm{(b) } \left(\alpha - \frac{1}{\alpha^2}\right)\left(\beta - \frac{1}{\beta^2}\right)[/imath]
Thank you!
