
Algebraic Errors
This is sample work of factorising with fractions in an inequality. I've been told that the 3rd line is incorrect, as $\displaystyle a^2+b^2$ cannot be factored over a real number. Can anyone help me determine if the factoring simply stops at the second line, or is there a correct way to continue?
Many thanks.
$\displaystyle \frac{a^2+b^2}{2} \geq ab$
$\displaystyle (a^2 + b^2/ 2)  ab$ > 0
$\displaystyle \frac{(a+b)(ab)}{2}ab\geq0$
$\displaystyle \frac{a^2ab+ab+b^2}{2}ab\geq0$
$\displaystyle \frac{a^2+b^22ab}{2}\geq0$
$\displaystyle (a^2  2ab + b^2)/2$ > 0
$\displaystyle \frac{(ab)^2}{2}\geq0$

Re: Algebraic Errors
Note that:
$\displaystyle (ab)(a+b) = a^2b^2$

Re: Algebraic Errors
Ah, ok I see it now. Thanks.