For all real numbers a and b, 2a*b = a^2+b^2.
True or false? If false, explain your reasoning.
I'm pretty sure this is false, but I'm not sure how I would explain that?
let a = 1
let b = 2
2 a b = 4
a^2+b^2 = 1+4 = 5
4 is not 5
find two numbers that don't work
To determine if the equation is true or false, we can start by testing it with specific numbers for "a" and "b." Let's choose a = 1 and b = 2:
Using the equation,
2a * b = a^2 + b^2
Substituting the values,
2 * 1 * 2 = 1^2 + 2^2
4 = 1 + 4
4 = 5
Since 4 is not equal to 5, the equation does not hold true for the values of a = 1 and b = 2. Therefore, we can conclude that the equation is false.
To further explain the reasoning, the equation states that for all real numbers "a" and "b," their product multiplied by 2 is equal to the sum of their squares. However, this is not true for all real numbers. By providing a counterexample, where a = 1 and b = 2 resulting in 4 = 5, we demonstrate that the equation does not hold true universally.