How does − 2 − 2 2 + 2 simplify to 1 − 2 I've the answer for a question in my textbook to be: − 2 − 2 2 + 2 which i've then simplifed to: − 3 − 2 2 However my textbook states − 2 − 2 2 + 2 = 1 − 2 How is this?

Question

How does   −                    2        −                  2                            2        +                  2                     simplify to   1  −      2  I&#039;ve the answer for a question in my textbook to be:    −                    2        −                  2                            2        +                  2                     which i&#039;ve then simplifed to:   −      3    −    2          2      However my textbook states   −                    2        −                  2                            2        +                  2                      =  1  −      2  How is this?

Louis Lawrence · Accepted Answer

2      −              2                    2      +              2              =            2      −              2                    2      +              2                        2      −              2                    2      −              2              =                    (        2        −                  2                )                    2              2  so                    2        −                  2                            2        +                  2                      =            2      −              2                    2        =      2    −  1

Liberty Mack · Accepted Answer

Alternatively, we can say   x  =  −                    2        −                  2                            2        +                  2                     . We can say that       x    2    =  −            2      −              2                    2      +              2                ⟹    −  (  2  +      2    )      x    2    +  (  −  2  +      2    )  =  0  We can now apply the quadratic formula and discard the negative root to obtain that  x  =  −            2              2                    4      +      2              2              =  −            2              2      +              2              =  −      2          2      +      2              2              =  −      1          1      +              2              =  1  −      2    .

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