Evaluate this !

Algebra Level 3

Evaluate .

( 63 b − 42 a ) 3 + ( 51 + 42 a ) 3 + ( − 51 − 63 b ) 3 ( 51 + 42 a ) ( 63 b − 42 a ) ( − 51 − 63 b ) \cfrac { (63b - 42a)^{ 3 }+(51+42a)^{ 3 }+(-51-63b)^{ 3 } }{ (51+42a)(63b-42a)(-51-63b) }


The answer is 3.

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

You can evaluate it in a simple way , by the identity, if a+b+c=0 then a 3 + b 3 + c 3 = 3 a b c a{ }^{ 3 }+b{ }^{ 3 }+c{ }^{ 3 }=3abc Therefore , 3 ( 63 b − 42 a ) ( 51 + 42 a ) ( − 51 − 63 b ) ( 51 + 42 a ) ( 63 b − 42 a ) ( − 51 − 63 b ) \cfrac { 3(63b-42a)(51+42a)(-51-63b) }{ (51+42a)(63b-42a)(-51-63b) } =3

10 Helpful 0 Interesting 0 Brilliant 0 Confused

It's misprinted, written as -51-63 in the numerator..

A Former Brilliant Member - 6 years, 9 months ago

Log in to reply

Thanks. I've updated the question.

Calvin Lin Staff - 6 years, 9 months ago

Log in to reply

Your Welcome

A Former Brilliant Member - 6 years, 9 months ago

let a=b=0 lol

math man - 6 years, 9 months ago

Log in to reply

Then denominator becomes zero.

Let a=b=1

Godwin Tom George - 6 years, 8 months ago

Yeah took me 5 seconds to complete the question.

Ronak Agarwal - 6 years, 9 months ago

Log in to reply

But 6 seconds to me. But fine you are older and senior to me !!!!!!!!!!!!!!1

Abhisek Mohanty - 6 years, 2 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...