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2022 Mathematics Extension 2 Q13 (c) (i) | HSC Atlas

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2022TrialShort answer

Q13 (c) (i)

1 mark

Question

Prove for all real $a$ and $b$ that
$a^2+b^2\ge 2ab.$

Try the question before revealing the answer.

Solution

For real $a,b$ ,

(a-b)^2\ge 0.

Expanding gives

a^2-2ab+b^2\ge 0,

so

\boxed{a^2+b^2\ge 2ab}.

AI HSC Engine generated solution · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Proof

The Nature of ProofUse formal proof language, contradiction, counter-examples and rigorous arguments involving numbers and inequalities.

Source

Girraween 2022 4U Trial PaperGirraweenQuestion paper page 7View original source ↗

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