Algebraic Errors

**GrigOrig99** · October 24th 2012, 06:47 AM

This is sample work of factorising with fractions in an inequality. I've been told that the 3rd line is incorrect, as $a^2+b^2$ 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.

$\frac{a^2+b^2}{2} \geq ab$
$(a^2 + b^2/ 2) - ab$ > 0
$\frac{(a+b)(a-b)}{2}-ab\geq0$
$\frac{a^2-ab+ab+b^2}{2}-ab\geq0$
$\frac{a^2+b^2-2ab}{2}\geq0$
$(a^2 - 2ab + b^2)/2$ > 0
$\frac{(a-b)^2}{2}\geq0$

**Siron** · October 24th 2012, 07:14 AM

Note that:
$(a-b)(a+b) = a^2-b^2$

**GrigOrig99** · October 24th 2012, 07:41 AM

Ah, ok I see it now. Thanks.

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