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'Implicitly' printed from http://nrich.maths.org/
$X(r)$ is defined implicitly by the quadratic relationship
Part 1: Which of the
choices $r=1,-1,100$ give real values for $X(r)$?
Part 2: What is the range
of values of $r$ for which $X(r)$ takes real values?
What happens when $r=0$?
Part 3: Sketch the overall
shape of $X(r)$ against $r$ and find the maximum and minimum values
Note: You could numerically find
a sensible conjecture for the minimum and maximum values of $X(r)$,
but to prove this you will need to use calculus.