Pythagorean theoremThe Pythagorean theorem is typically written as a 2 + b 2 = c 2 where a and b are the two shorter sides (legs) of a right triangle and c is its longest side (the hypotenuse).Given the exponent powers c 2 × 1 / 2 = c, why cant I express " a = c − b".The correct answer given was c 2 − b 2

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Pythagorean theoremThe Pythagorean theorem is typically written as      a    2    +      b    2    =      c    2  where a and b are the two shorter sides (legs) of a right triangle and c is its longest side (the hypotenuse).Given the exponent powers       c          2            ×            1              /            2        =  c, why cant I express &quot;  a  =  c  −  b&quot;.The correct answer given was             c      2        −          b      2

timmeraared · Accepted Answer

You need to think more carefully about what is going on.Note that  25  =  9  +  16   or       3    2    +      4    2    =      5    2  but it is not true that  3  =  5  −  4instead it is true that  3  =            3      2        =            5      2        −          4      2      Using very simple examples as a check can help you to avoid mistakes, and also to see where the mistake is. But don&#039;t rely on them to replace formal arguments - sometimes simple cases miss the point.

vrotterigzl · Accepted Answer

That is because             c      2        −          b      2       is not in general equal to c−b.If you are raising things to a power, in general you can&#039;t do it term by term (just try some explicit examples to see why this is).In that particular case you can either write       a    2    =      c    2    −      b    2   or   a  =            c      2        −          b      2      .

Pythagorean theorem The Pythagorean theorem is typically written as a 2 </msup> +

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