Question

Given the function f(x) = 6x^2, what is the value of f(a+b)-f(a-b)/ab when a and b are both positive?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the value of f(a+b) - f(a-b)/ab, we need to substitute a and b into the function f(x) = 6x^2.

First, let's calculate f(a+b):
f(a+b) = 6(a+b)^2 = 6(a^2 + 2ab + b^2) = 6a^2 + 12ab + 6b^2.

Next, let's calculate f(a-b):
f(a-b) = 6(a-b)^2 = 6(a^2 - 2ab + b^2) = 6a^2 - 12ab + 6b^2.

Now, let's substitute these values into the expression (f(a+b) - f(a-b))/ab:

(f(a+b) - f(a-b))/ab = ((6a^2 + 12ab + 6b^2) - (6a^2 - 12ab + 6b^2))/ab
= (6a^2 + 12ab + 6b^2 - 6a^2 + 12ab - 6b^2)/ab
= (24ab)/ab
= 24.

Therefore, the value of f(a+b) - f(a-b)/ab when a and b are both positive is 24.