Question

if a3+b3+c3=3abc then the value of a+b+c where a not equal to b and c

Answer 1

Hi ,

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We know the algebraic identity ,

x³ + y³ + z³

= (x+y+z)(x²+y²+z²-xy-yz-zx) + 3xyz

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Now ,

a³ + b³ + c³ = 3abc ( given )

(a+b+c)(a²+b²+c²-ab-bc-ca)+3abc=3abc

(a + b + c)(a²+b²+c² - ab - bc - ca) = 0

a + b + c = 0

Or

a² + b² + c² - ab - bc - ca = 0

Required condition is ,

a + b + c = 0

Where ,

a ≠ b and a ≠ c

I hope this helps you.


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Answer 2

Hi,

Please see the attached file!


Thanks