LEARN · EXPLAIN · REVISE

Minimize the expression over positive x.

Read the idea, work independently, then explain what changed.

TOPIC 01

Quadratic functions, equations and inequalities: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

2x+\frac{200}x

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Check nonnegativity, apply AM–GM and verify attainable equality.

Hint 2

Include the coefficient two in the product.

Worked solution

Check nonnegativity, apply AM–GM and verify attainable equality.
Calculate or simplify this relation.
$2x+\frac{200}x\ge2\sqrt{400}=40;\quad x=10$
Equality concerns the complete two terms, not just x and 1/x.

The requested value is 40.

Checks and common pitfalls: Equality concerns the complete two terms, not just x and 1/x.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment