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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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Quartics

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

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Without Calculus

Given that u>0 and v>0 find the smallest possible value of 1/u + 1/v given that u + v = 5 by different methods.

Biggest Bendy

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How would the area change as one of the angles is changed?

You could try splitting the quadrilateral into two triangles. Can you find an expression for the length of the diagonal in two different ways?