Question

Anyone getting bored?
try this :
If a³ + b³ = 0 , then the value of log (a + b) – 0.5(log a + log b + log 3) is equal to ??

Answer 1

just for safety:
a\(\ne\)b
a\(\ne\)-b

Answer 2

\[a^3 + b^3 = (a + b)(a^2 - ab + b^2)\]So,\[(a + b)(a^2 - ab + b^2) = 0\]Dividing both sides by a + b,\[a^2 - ab + b^ 2 = 0\]Since \(a^2 - 2ab + b^2 = (a - b)^2\), we have,\[a^2 - 2ab + b^2 +ab = 0\]\[(a - b)^2 + ab = 0\]\[(a - b)^2 = - ab\]\[a^2 + b^2 = ab\]One such case is a = 0 and b = 0, but you haven't allowed that. :(

Answer 3

hmm....nice try
no other formula for a^3+b^3 ?

Answer 4

Are you sure that your question is correct? If a^3 + b^3=0, then either a=-b or a=b=0.... :\ (because x^3 if a one one function)

Answer 5

yes, question is correct.

Answer 6

0

Answer 7

how ?

Answer 8

continuing from parthkohli,