If a1/3 + b1/3 + c1/3 = 0, then (a + b + c)6 is equal to:
Show answer & explanation
Correct answer: A
Explanation
Correct Answer is option 1 i.e. 729a2b2c2
|
Concept |
Understanding |
Application |
|
If x + y + z = 0 then x3 + y3 + z3 = 3xyz |
Given a1/3 + b1/3 + c1/3 = 0
|
Then (a1/3)3 + (b1/3)3 + (c1/3)3 = 3 a1/3 b1/3 c1/3 ⇒ (a + b + c) = 3 a1/3 b1/3 c1/3 Taking cube ⇒ (a + b + c)3 = 27abc Squaring both sides: ⇒ (a + b + c)6 = 729a2b2c2 |