Prove the Conditional Equation 'If a + b + c = 0, Then a^3 + b^3 + c^3 = 3abc' - Easy Tutorial

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Thank you very much sir keep going and stay safe

Blackjac

I think my way is a little easier. From a+b+c=0 transpose the c to the right side and get a+b=-c then cube both sides you get a^3+b^3+3ab(a+b)=-c^3, replace a+b with -c you get a^3+b^3-3abc=-c^3 then transpose -c^3 to the left side and -3abc to the right side and the final result is the desired form a^3+b^3+c^3= 3abc. Much quicker wont you agree?

johngreen

I used the general formula for (a+b+c)^3 = a^3 + b^3 + c^3 +3(a+b)(b+c)(c+a) and then substituted a+b=-c and so on
We get -3abc which will be positive when we move it to the other side of the equality.

If any has a confusion regarding the formula, you can make it on your own by grouping terms like

(a+b+c)^3 = {(a+b) + c }^3 and the expand the terms using expansion formula for (x+y)^3 and then group the like terms.

santanuganguly

Definitely an easy tutorial! I recalled the conditional equations when I was in college!

iZAPMath

Very nice proof as it doesn't depend on memory work. Another way of doing it is to realise that a^3+b^3+c^3- 3abc is divisible by a+b+c and to know the other factor or else to divide in to get the other factor if you don't remember it. The method employed in this video is much better.

johnbrennan

We can show, with a method called Newton - sums that in x^3 + wx + p = 0 , the the sum of the qube of the roots is -3p [a^3 +b^3 +c^3]

זאבגלברד

How to prove: if a<b<c then a<(a+b+c)/3<c

VedroNebo-bjyw

Thanku sir n waiting for more interesting videos 👍👍

pragatiagrawal

so nice sir, please make a video on logarithm.

sanghamitrapradhan

a^3 + b^3 + c^3 − 3abc = (a + b + c)(a^2 + b^2 + c^2 − ab − bc − ac).
This identity can be easily proved using Viet's rules for the cubic equation.

golddddus

For what values does the equality hold. Is it a=b=c=0?

unknownpersonlionesse

Thank you so much sir this helped me a lot =D

ac

thanks sir.
waiting for nest vedio.
🌹🌹🌹

govindashit

Sir what is the answer of a^3+b^3+c^3 formula

mdmotaher

OK !
But it doesnot work with numbers as : 2^3 + 3^3 + 4^3

j.c

If a+b+c=0 show that a^3+b^3+c^3=27 abc

mathematicswithaliyasmalay

Tôi làm được vận bản hay như hiếp khỏi lắc dan

vubuivanphong

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