prove that n^2 − 6n + 10 is always positive- completing the square Watch

wishiwerenthere
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#1
I'm resitting A-level maths and writing notes.

My thoughts are:
(n-3)^2 will always be positive (because squared numbers are), apart from when n=3 (when the value of the bracket will be 0), in which case the "+1" makes it positive.

Is this a valid argument/line of reasoning?
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mqb2766
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Spot on, thats a key thing about completing the square
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wishiwerenthere
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(Original post by mqb2766)
Spot on, that's a key thing about completing the square
Lovely, thank you
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mqb2766
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To be a bit less wordy, you could say
n^2 - 6n + 10 = (n-3)^2 + 1 >= 1 > 0
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