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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 ?

Exponential Trend

Age 16 to 18 Challenge Level:

The function is undefined for $x=0$ but we need to find the limiting value as $x \to 0$ to answer the question.