1. Teacher's Notes Topic: Proof L7 Is the geometric mean (when it exists) always between the two numbers? When you have one positive and one negative number there is a problem with this, but what if both numbers are negative? What if one number is zero? Geometric mean (a) For the two numbers 10 and x, the geometric mean is 30 What is the value of x ? Example: geometric mean of 4 and 9 Multiply the two numbers together, then find the square root of the result. Here is the rule to find the geometric mean of two numbers. (b) Reena says: 'For the two numbers -2 and 8, it is impossible to find the geometric mean.' Is Reena correct? Explain your answer.

2. Here is the rule to find the geometric mean of two numbers. Geometric mean Multiply the two numbers together, then find the square root of the result. Example: geometric mean of 4 and 9 (a) For the two numbers 10 and x, the geometric mean is 30 What is the value of x ?

3. (b) Reena says: 'For the two numbers -2 and 8, it is impossible to find the geometric mean.' Is Reena correct? Explain your answer.