I have this equation: x 2 + ( x − 7 ) 2 = 13 2 Why can't squaring the whole equation be used to solve it? x 2 + ( x − 7 ) 2 = 13 2 ≡ x + x − 7 = 13

Question

I have this equation:      x    2    +  (  x  −  7      )    2    =      13    2  Why can&#039;t squaring the whole equation be used to solve it?            x      2        +    (    x    −    7          )      2        =          13      2        ≡  x  +  x  −  7  =  13

talhekh · Accepted Answer

Following your approach, we would get x=10.But neither       10    2    +      3    2    =      13    2  , nor             10      2        +          3      2        =  13You can indeed &quot;square root&quot; the equation (with some care for the signs), but you may not &quot;square root&quot; a sum.Indeed,   (  a  +  b      )    2    =      a    2    +  2  a  b  +      b    2    ≠      a    2    +      b    2

I have this equation: x 2 </msup> + ( x − 7

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