Find x 2 y 2 + y 2 x 2 If x y + y x = 3

Question

Find             x      2              y      2       +             y      2              x      2      If       x    y   +       y    x   = 3

poquetahr · Accepted Answer

x          y                +                  y          x                =        3                            ⟹                              (                          x              y                        +                          y              x                        )                    2                =        9                                          ⟹                              x            2                                y            2                          +                              y            2                                x            2                          =        9        −        2        =        7

Gretchen Schwartz · Accepted Answer

Hint: Look at:            (              x        y            +              y        x            )        2    =      3    2    =  9Why to look at this? We know if we expand we will have a   (      x    y        )    2    =            x      2              y      2       term and a   (      y    x        )    2    =            y      2              x      2       term so this might be worth a try.

Find x 2 </msup> y 2 </msup> </mfrac> +

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