Question

the sum of x square - y square,y square- z square and z square- x square is ​

Answer 1

SOLUTION

CORRECT QUESTION

The sum of

$\sf {x}^{2} - {y}^{2} \: , \: {y}^{2} - {z}^{2} \: , \: {z}^{2} - {x}^{2}$

EVALUATION

Here the given expressions are

$\sf {x}^{2} - {y}^{2} \: , \: {y}^{2} - {z}^{2} \: , \: {z}^{2} - {x}^{2}$

On addition we get

$\sf = ( {x}^{2} - {y}^{2} \: ) + ( \: {y}^{2} - {z}^{2} )\: + (\: {z}^{2} - {x}^{2} )$

$\sf = {x}^{2} - {x}^{2} + {y}^{2} - {y}^{2} + {z}^{2} - {z}^{2}$

$\sf = 0 + 0 + 0$

$\sf = 0$

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