Question

If `a^2 + b^2 = 4` and `(a-b)^2 =2`, what is the value of `ab`?

Answer 1

The value of `ab` is `1`.

Explanation:

We can expand `(a- b)^2` to see that `(a- b)^2 = a^2 - 2ab + b^2`, thus `a^2 + b^2 - 2ab = 2`.

It follows that `a^2 + b^2 = 2 + 2ab`, and since we're given that `a^2+ b^2 = 4`, we can say `4 = 2 + 2ab`. Doing a little algebra we get

`4 = 2(1 + ab)`

`2 = 1 + ab`

`ab = 1`

Hopefully this helps!