I am going through previous algebra exercises that I had performed from a textbook in Matlab.
However, although I am certain that my results are correct, Matlab is throwing up different answers to mine.
Examples of some of these questions are:
- $$ 16x^2 - 40xy + 25y^2 = 0$$
For this, I get factors of $$ (4x - 5y)^2 = 0$$
- $$ 5x^2 + 13x + 6 = 0$$
For this, I get factors of $$ (5x + 3)(x + 2) = 0$$
- $$ 2x^2 - 11x + 12 = 0$$
For that, I get factors of $$ (2x - 3)(x - 4) = 0$$
And the results produced by Matlab are shown below:
Ultimately, what I am seeking is just confirmation that my answers are correct and that Matlab is just displaying other possible solutions!
Your algebra is simply wrong for part 1.
$$ (3x-4)(2y+5) = 6xy - 8y + 15x - 20 $$ which is not at all the same as $$16^2−40+25^2$$.
In fact, $16^2−40xy+25^2 = 0$ actually factors as $$ (4x - 5y)^2 = 0 $$ for which any pair $(x,y) = (a, -\frac{5}{4}a)$ is a solution.
I don't understand Matlab's answer that $y$ is $0$ or $0$, however.
Part 2: Your algebra is right here, but Matlab's answer is baffling. No positive value of $x$ can yield a root of that equation, because all three terms are positive, and hence cannot sum to zero. Perhaps "solve" doesn't work the way you (and I) may think it does. Then again, when I tried running it, Matlab gave the answers $-2, -3/5$. Did you remember to declare
xsymbolic withsym x?