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Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

Overturning Fracsum

Can you solve the system of equations to find the values of x, y and z?

Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

Leonardo's Problem

Age 14 to 18
Challenge Level

Why do this problem?

The problem requires interpretiation of the information given and the creation of equations from that information. Discussion of the ways of interpreting the information could help to develop team working and communication skills.

Possible approach

You might give learners some time to work independently on this problem then get them to share their ideas in small groups or pairs.

Key questions

What are the unknowns?

What equations an we write down based on the information given?

Possible support

You might first try the easier non-standard simultaneous equations problems Always Two and System Speak .