Question

if a+b+c=0,then what is the value of a³ b³ c³

Answer 1

{a}^{3}  + b {}^{3}  +  {c}^{3} - 3abc  = (a + b + c)( {a}^{2}  +  {b}^{2}  +  {c}^{2}   - ab - bc - ac)

but a +b + c is 0 so

{a}^{3}  +  {b}^{3}  +  {c}^{3}  - 3abc \:  = (0)( {a}^{2}  +  {b}^{2}  +  {c}^{2}  - ab - bc - ac) \\  =  {a}^{3}  +  {b}^{3}  +  {c}^{3}  - 3abc = 0 \\  {a}^{3}  +  {b}^{3}  +  {c}^{3}  = 3abc

hope it helps

Answer 2

Hey there!!


This is the question of class 9,


Chapter :- Algebraic identities.



➡ Given :-,


→ a + b + c = 0.



➡ To Find :-


→ a³ + b³ + c³ .



➡ Solution:-



▶ By using an identity :-


→ a³ + b³ + c³ - 3abc = ( a + b + c ) ( a²+ b² + c² - ab - bc - ca ).


Now, put the value of ( a + b + c ) in the identity.


=> a³ + b³ + c³ - 3abc = ( 0 ) ( a²+ b² + c² - ab - bc - ca ).



We know that if any number is multiplied by 0, then the value came out is 0.


→ Here, ( a²+ b² + c² - ab - bc - ca ) is the number.


→ So, it is multiplied by 0, then the value is 0.


=> a³ + b³ + c³ - 3abc = 0.


Move the - 3abc to the RHS side, the minus value changes to plus.



=> a³ + b³ + c³ = 3abc.


✔✔ Hence, it is solved ✅✅.

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THANKS


#BeBrainly.