Can you show this?Show that 2 x 2 + 1 x = 2 + 1 / x 2 .This seems like basic algebra, but I can't really manage to deal with the sqrt sign and prove this.

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Can you show this?Show that            2              x        2            +      1        x    =      2    +    1          /              x      2        .This seems like basic algebra, but I can&#039;t really manage to deal with the sqrt sign and prove this.

Andrejkoxg · Accepted Answer

I think it&#039;s wrong.Try   x  =  −  1.By the way,            2              x        2            +      1        x    =      2    +          1              x        2            for x&amp;gt;0 and            2              x        2            +      1        x    =  −      2    +          1              x        2            for x&amp;lt;0.The both equalities we can write so:      2    +          1              x        2              =            2              x        2            +      1                      x        2              =            2              x        2            +      1                      |            x              |

Frida Faulkner · Accepted Answer

1)   x  &amp;gt;  0  , the equality is OK.2)   x  &amp;lt;  0, LHS is negative, RHS positive.LHS:                     2                  x          2                +        1            x        =                              x          2                (        2        +                              1                          x              2                                      )            x        =                              |                x                  |                          2          +                                    1                              x                2                                                        x        =                              |                x                  |                    x            2    +                  1                  x          2                      .Note:                              |                x                  |                    x        =  1 for   x  &amp;gt;  0  ;                              |                x                  |                    x        =  −  1 for   x  &amp;lt;  0.

Can you show this? (sqrt(2x^2+1))/(x)=sqrt(2+1/x^2).This seems like basic algebra, but I can't really manage to deal with the sqrt sign and prove this.

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