Question

x+y+z=0 prove that x3 + y3+ z3 = 3 xyz

Answer 1

Its a formula X3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-xz). If we put x+y+z=0 so

X3+y3+z3-3xyz=0

X3+y3+z3=3xyz

Answer 2

Hey there!!

This is the question of class 9,

Chapter :- Algebraic identities.


➡ Given :-,

→ x + y + z = 0.


➡ To prove :-

→ x³ + y³ + z³ = 3xyz.


➡ Solution:-


▶ By using an identity :-

→ x³ + y³ + z³ - 3xyz = ( x + y + z ) ( x²+ y² + z² - xy - yz - zx ).

Now, put the value of ( x + y + z ) in the identity.

=> x³ + y³ + z³ - 3xyz = ( 0 ) ( x²+ y² + z² - xy - yz - zx ).


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

→ Here, ( x²+ y² + z² - xy - yz - zx ) is the number.

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

=> x³ + y³ + z³ - 3xyz = 0.

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


=> x³ + y³ + z³ = 3xyz.

✔✔ Hence, it is proved ✅✅.

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#BeBrainly.