Question

Verify the following: (a²-b²)(a²+b²)+(b²-c²)(b²+c²)+(c²-a²)(c²+a²)=0
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Answer 1

LHS=(a⁴-b⁴)+(b⁴-c⁴)+(c⁴-a⁴) {open all brackets}

= a⁴-b⁴+b⁴-c⁴+c⁴-a⁴ {now everything will get cancelled)

= 0

RHS= 0

LHS=RHS

hence verified!

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Answer 2

Answer:

Solution :

LHS -

(a² - b²)(a² + b²) + (b² - c²)(b² + c²) + (c² + a²)(c² - a²)

=> a²(a² + b²) - b²(a² + b²) + b²(b² + c²) - c²(b² - c²) + c²(c² - a²) + a²(c² - a²)

=> a⁴ + a²b² - b²a² - b⁴ + b⁴ + b²c² - c²b² - c²a² + a²c² - a⁴

=> a⁴ + [ a²b² - b²a² ] - b⁴ + b⁴ + [ b²c² - c²b² ] - c⁴ + c⁴ - [c²a² - a²c²] - a⁴

=> a⁴ - b⁴ + b⁴ - c⁴ + c⁴ - a⁴

=> 0

Hence Verified

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