Two real numbers have a fixed sum of 18. Let the first number be x and the second number be (18−x).
Answer the following questions.
(i) Form the quadratic equation in x that the two numbers must satisfy.
(ii) Derive an expression for the discriminant Δ of the equation obtained in part (i) and hence show that the two numbers are real only when their product P satisfies P≤81.
(iii) If the product of the two numbers is 70, determine whether such numbers exist. Give reason for your answer based on the result of part (ii).