Final answer:
To show that a² + b² = 0 implies a = 0 and/or b = 0, we use the fact that a squared number in the real numbers is always non-negative. Since both a² and b² must be non-negative for their sum to be zero, it follows that a and b must both be zero.
Step-by-step explanation:
To prove that if a and b are real numbers such that a² + b² = 0, then a = 0 and/or b = 0, we can use the properties of real numbers and the nature of squared terms.
In the realm of real numbers, a number squared is always non-negative, meaning it is either positive or zero. This is because the product of two positive numbers or two negative numbers is positive, and zero squared is zero. For the equation a² + b² = 0, both terms a² and b² are non-negative and their sum is zero. This implies that both a² and b² must separately equal zero. Therefore, a = 0 and b = 0.
Conclusively, the only possibility for the sum of two squared real numbers to equal zero is if both of those numbers themselves equal zero.