Really tough

Algebra Level 4

( b − c a + c − a b + a − b c ) ( a b − c + b c − a + c a − b ) \large{\left(\dfrac {b-c}{a}+\dfrac {c-a}{b}+\dfrac {a-b}{c}\right)\left(\dfrac {a}{b-c}+\dfrac {b}{c-a}+\dfrac {c}{a-b}\right)}

If a + b + c = 0 a+b+c=0 , then find the value of the expression above.


The answer is 9.

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Atul Shivam by Atul Shivam , 23, India

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3 solutions

汶良 林
Oct 19, 2015

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Nivedit Jain
Jun 2, 2017

Better way to do it take a,b and c as cube roots of unity.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Innovative approach. Since the problem doesn't state anything about the numbers a,b,c one could assume them to be anything.

Nishant Sharma - 2 years, 12 months ago
Rhealyn Alba
Oct 18, 2015

Assign values of a, b and c that could give an answer 0 when added. As for me, I've used a= 3, b= 2, c= -5. Then substituted them all to the expression. It gives an answer of 9. :)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I think you should generalise it for all values,without taking any specific value,thanks

Atul Shivam - 5 years, 7 months ago

One can assign any value for a, b, c, if it satisfies a+b+c=0 and none equal to 0 or to one another.( Divide by 0 not valid.)
That will give the answer. But not good as proof.

Niranjan Khanderia - 2 years, 7 months ago

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