Quadratic equations

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

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

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel lines are 1 unit and 2 units.

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Sketch the graphs for this implicitly defined family of functions.

Explore the geometry of these dart and kite shapes!

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

Is the mean of the squares of two numbers greater than, or less than, the square of their means?