You are right.aces021 wrote:4x^2=y^2-3^2
Is it possible to take the square root of the right side?
Since they are being subtracted our only option is to put it in this form (y-3)(y+3). We are not allowed to do √y^2-3^2 = y-3. Is this correct?
We cannot take the expression y² - 3² and rewrite it as (some expression)(the same expression). Therefore, we can't find a "nice" square root of y² - 3²
The best we can do is rewrite it as (y + 3)(y - 3)
Also note that we can easily confirm whether or not √(y² - 3²) = (y - 3)
Aside: Since √25 = 5, we know that (5)(5) = 25
Likewise, since √49 = 7, we know that (7)(7) = 49
So, IF √(y² - 3²) = (y - 3), then it must be true that (y - 3)(y - 3) = y² - 3²
HOWEVER, (y - 3)(y - 3) = y² - 6y + 9
So, √(y² - 3²) ≠(y - 3)
Cheers,
Brent
