ATLASBetaSearch subjects

Subjects

Ancient HistoryComing soon

Biology Business Studies

ChemistryComing soon

EngineeringComing soon

English Advanced English Ext 1 English Standard

English StudiesComing soon

Enterprise ComputingComing soon

Health & MovementComing soon

Legal Studies Maths Advanced Mathematics Ext 1 Mathematics Ext 2

Maths Standard 1Coming soon

Maths Standard 2Coming soon

Modern HistoryComing soon

Physics Religion I Religion II

Visual ArtsComing soon

Save your favourites

Accounts and progress tracking are coming later.

Coming later

2023 Mathematics Extension 2 Q14 (b) (ii) | HSC Atlas

← Back to Mathematics Extension 2 questions

2023TrialShort answer

Q14 (b) (ii)

1 mark

Question

Given $a$ , $b$ , $c$ are positive real numbers, hence or otherwise, prove that

a^3+b^3+c^3\ge3abc.

Try the question before revealing the answer.

Solution

(a+b+c)(a^2+b^2+c^2)\ge(a+b+c)(ab+bc+ca)

Expanded both sides and simplify, we obtain

a^3+b^3+c^3\ge3abc

Supplied marking guidance · 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

James Ruse 2023 4U Trial PaperJames RuseQuestion paper page 10Guidance page 29View original source ↗

Spot a problem? Send feedback

WebsiteWhat needs attention?Tell us what looks wrong

Please do not include your name, school, or other personal details.