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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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How Many Solutions?

Find all the solutions to the this equation.

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After Thought

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

Curve Match

Stage: 5 Challenge Level: Challenge Level:1
The green graph should be straightforward to identify.
A little bit of numerical detective work should help you to identify which axis is which.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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