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Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

Target Six

Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.

Power Quady

Age 16 to 18
Challenge Level

Find all real solutions of the equation
$$(x^2-7x+11)^{(x^2-11x+30)} = 1.$$

You may also be interested in the problem Mega Quadratic Equations.