(adsbygoogle = window.adsbygoogle || []).push({}); How come the proof is "wrong" if I do it backwards?

1. The problem statement, all variables and given/known data

Let x >0. Then show that

[tex]x + 1/x \geq 2[/tex]

and that the equality holds when x is 1

I got full marks on this, but remarked by my TA that I should do it backwards next time

Proof

[tex]x + 1/x \geq 2 \iff x^2 + 1 \geq 2x \iff x^2 - 2x + 1 \geq 0 \iff (x - 1)^2 \geq 0[/tex]

Also the equality is true if x = 1

[tex](1 - 1)^2 = 0^2 \geq 0[/tex]

Q.E.D

My TA said I should start with [tex] (x - 1)^2 \geq 0[/tex] and go backwards. Why? If this was on an exam, how could I make up so much space and then erase and go back??

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# How come the proof is wrong if I do it backwards?

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