2020HSCShort answer

Q13 (c) (ii)

1 mark

Question

Prove that
$p^2+4q^2\geq4pq.$

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	1

Sample answer:

Put $a=p^2$ , $b=(2q)^2$ .

\frac{p^2+4q^2}{2}\ge\sqrt{4p^2q^2}

p^2+4q^2\ge4pq

Supplied marking guidance · human reviewed

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

Syllabus alignment

Working MathematicallyProof

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

Spot a problem? Send feedback