I'm using the quadratic equation and I understand how to use it, but the format my text book gives the answers in is what I don't understand.
If I have (2+/-Sqrt(8))/2
I know that x can either equal 2.41 or -0.14
However, my textbook is giving me the answers as 1+Sqrt(2) and 1-Sqrt(2)
I understand where the 1+/- comes from, but how are they getting Sqrt(2)?
I hope you can understamd what I mean. I'm confised, so I wasn't sure how to word the question correctly, but I hope you can see where I am having trouble.
Thank you.
sqrt(8) can be simplified because 8 = 2^3
I understand your question. The discrepancy in the answers is due to simplifying the expression involving the square root. Let's break it down step by step to understand how to get the textbook's answers.
Starting with the expression (2 +/- sqrt(8))/2:
1. Simplify the square root of 8:
sqrt(8) = sqrt(4*2) = sqrt(4) * sqrt(2) = 2 * sqrt(2).
2. Replace sqrt(8) in the original expression:
(2 +/- 2 * sqrt(2))/2.
3. Simplify the expression inside the brackets by factoring out the common factor of 2:
2(1 +/- sqrt(2))/2.
4. Cancel out the common factors of 2:
1 +/- sqrt(2).
So, the correct simplified form of (2 +/- sqrt(8))/2 is 1 +/- sqrt(2). This explains why your textbook is giving you the answers as 1 + sqrt(2) and 1 - sqrt(2).