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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?

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Overturning Fracsum

Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7

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Bang's Theorem

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

Leonardo's Problem

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 .