Posted by markmorse@nocharge.com (64.40.61.194) on October 08, 2003 at 07:41:40:
In Reply to: quadratic formula posted by on October 08, 2003 at 03:32:58:
You got:
[4 + sqrt(76)]/6 and [4 - sqrt(76)]/6
That's correct so far, but it's not simplified.
76 = 4 * 19, so sqrt(76) = sqrt(4) * sqrt(19) = 2 sqrt(19).
If we replace sqrt(76) with 2 sqrt(19), we can factor out a 2 from the numerator:
[4 + sqrt(76)] = [4 + 2 sqrt(19)] = 2[2 + sqrt(19)]
Of course, the denominator is 2 * 3, so the 2 in the numerator which we factored out will cancel with the 2 in the denominator.
[2 + sqrt(19)]/3
[2 - sqrt(19)]/3
This is the simplified result which matches the other answer you have.
Let us know if you need more help with this. Try to explain what part(s) you don't understand.
~ Mark