When is x / y 2 equal to x / y?The solution to the quadratics is given by r = − b 2 a ± b 2 − 4 a c 4 a 2 , which is shortened to r = − b 2 a ± b 2 − 4 a c 2 a , but I'm wondering how if this is justified, given that 4 a 2 can be negative if a ∈ C , and x y ≠ x y if x and y are negative, but given that we have a 2 , is this justified?Is x / y 2 = x / y? Is r = − b 2 a ± b 2 − 4 a c 2 a always true?

Question

When is       x          /              y      2       equal to       x        /    y?The solution to the quadratics is given by  r  =  −            b              2        a              ±                                          b            2                    −          4          a          c                          4                      a            2                              , which is shortened to   r  =  −            b              2        a              ±                              b          2                −        4        a        c                    2        a            , but I&#039;m wondering how if this is justified, given that   4      a    2   can be negative if   a  ∈      C  , and                     x        y              ≠                    x                    y             if x and y are negative, but given that we have       a    2  , is this justified?Is       x          /              y      2        =      x        /    y? Is   r  =  −            b              2        a              ±                              b          2                −        4        a        c                    2        a             always true?

Syllingbs · Accepted Answer

When   y  &amp;gt;  0, you have            x              y        2              =            x                      y        2              =            x        y    .When   y  &amp;lt;  0, you have            x              y        2              =            x                      y        2              =            x              −      y        .

uznosititr · Accepted Answer

The two possible values of       4          a      2       for complex   a differ only by a sign (one is   2  a, the other is   −  2  a), so the set of solutions given by the formula  r  =  −            b              2        a              ±                              b          2                −        4        a        c                    2        a            is the same as that given by the formula  r  =  −            b              2        a              ±                                          b            2                    −          4          a          c                          4                      a            2                                .(The &quot;plus&quot; in one formula may or may not correspond to &quot;plus&quot; in the other one, but this doesn&#039;t matter.)

When is <msqrt> x <mrow class="MJX-TeXAtom-ORD"> / </mrow> y 2

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