Question

The sum of x² – y², y² – z² and z² – x² is​

Answer 1

Step-by-step explanation:

(x²-y²) + (y²-z²) + (z²-x²)

= x² - y² + y² + z² - x²

= 0

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Answer 2

Given,

• x² – y²
• y² – z²
• z² – x²

To find,

• We have to find the sum of x² – y², y² – z², and z² – x².

Solution,

We can simply find the sum of x² – y², y² – z², and z² – x² by adding the given expressions:

then,   x² – y²+ y² – z² + z² – x²

In the above expression, x² gets canceled with - x², similarly, y² gets canceled with -y², and  z² gets canceled with -z².  

       = x² – y²+ y² – z² + z² – x²

       = 0

then, we are left with '0'.

∴ The sum of  x² – y², y² – z², and z² – x² is​ 0.

Hence, the sum of  x² – y², y² – z², and z² – x² is​ 0.