What's the value of x if 1 x + 1 y + z = 1 2 and 1 y + 1 z + x = 1 3 and 1 z + 1 x + y = 1 4 . Find the value of x.

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What&#039;s the value of   x if       1    x    +      1          y      +      z        =      1    2   and       1    y    +      1          z      +      x        =      1    3   and       1    z    +      1          x      +      y        =      1    4  . Find the value of x.

Illuddybopylu · Accepted Answer

I suggest to go for   X  =      1    x  ,   Y  =      1    y   and   Z  =      1    z   because it has the advantage to simplify the denominators.The equations become                    X        Y        +        Y        Z        +        Z        X                    Y        +        Z              =            1      2          ;                      X        Y        +        Y        Z        +        Z        X                    X        +        Z              =            1      3          ;                      X        Y        +        Y        Z        +        Z        X                    X        +        Y              =            1      4      And it gives a simple system to solve      {                            Y          +          Z          =          2          k                                      X          +          Z          =          3          k                                      X          +          Y          =          4          k                                      X          Y          +          Y          Z          +          Z          X          =          k                        For instance   (  2  )  −  (  1  ) gives   X  −  Y  =  k and reporting in   (  3  ) gives   2  Y  =  3  k.This is all similar easy calculation and we end up with   X  =      5    2    k  ,  Y  =      3    2    k  ,  Z  =      1    2    k and                     23                  k          2                    4        =  kFinally   x  =      1    X    =      2    5    ×      23    4    =      23    10  .

Given x, y, z in RR, such that 1/x+1/(y+z)=1/2 and 1/y+1/(z+x)=1/3 and 1/z+1/(x+y)=1/4. Find the value of x.

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