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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?

How Many Solutions?

Find all the solutions to the this equation.

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:

In order to differentiate this function and to find the turning points express it in the form $x^{1/x} = e^{1/x \log x}.$