Maths Olympiad - Algebra 1

Question:

where a and b are real numbers.

Find the maximum possible value of (a - 5b).

Answer:

Since the square of any number cannot be negative, the minimum value of

is ZERO.

(*Since its minimum value would make the resulting number the maximum possible value because it is multiplied by a negative number -4)

Therefore, the maximum possible value of (a - 5b)

= - 4 (0 - 125)

= 500