A longer equality

Algebra Level 4

If distinct, non-zero reals a , b , c a, b, c are such that a + b + c = 0 a+b+c=0 , what is the value of

P = ( a − b c + b − c a + c − a b ) ( c a − b + a b − c + b c − a ) P=\left( \frac { a-b }{ c } +\frac { b-c }{ a } +\frac { c-a }{ b } \right) \left( \frac { c }{ a-b } +\frac { a }{ b-c } +\frac { b }{ c-a } \right) ?


The answer is 9.00.

Linkin Duck by Linkin Duck , 33, Vietnam

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2 solutions

Steven Jim
Jun 8, 2017

[Not a solution]

Same problem with 5 solutions

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Siva Bathula
Jun 8, 2017

@Linkin Duck The variables are distinct and non-zero, if any two of a,b,c are equal then P = 0

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You are right, I'll edit that problem.

Linkin Duck - 4 years ago

You mean "undefined"?

Steven Jim - 4 years ago

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