Final answer:
The values of x and y for which a² = a are found in options c) x = 0, y = 0 and d) x = 1, y = 1, as they correspond to a being either 0 or 1, which are the only real numbers for which the equation a² = a hold true.
Step-by-step explanation:
The student has asked to determine the values of x and y for which a² = a. If we assume a to be a real number, the equation implies that either a = 0 or a = 1, because those are the only real numbers for which the equation a² = a hold true. Therefore, we must find the values of x and y that correspond to a being either 0 or 1.
To find the correct values, let's analyze the given options:
- a) x = 0, y = 1
- b) x = 1, y = 0
- c) x = 0, y = 0
- d) x = 1, y = 1
Options c) x = 0, y = 0 and d) x = 1, y = 1 represent the scenarios where a equal 0 and 1, respectively, fulfilling the condition of our original equation, a² = a.