Quadratic equations

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.

Find a connection between the shape of a special ellipse and an infinite string of nested square roots.

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

Can you find the solution to this algebraic inequality?

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.

Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.

Given a regular pentagon, can you find the distance between two non-adjacent vertices?

A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.