1.

If a\(\frac{1}{3}\)+b\(\frac{1}{3}\) + c\(\frac{1}{3}\) = 0, thenA. a+b+ c =0B. (a+b+ c)3 = 27abcC. a+b+ c = 3abcD. a3+b3+ c3 = 0

Answer»

a\(\frac{1}{3}\) + b\(\frac{1}{3}\) + c\(\frac{1}{3}\) = 0

⇒ a\(\frac{1}{3}\) + b\(\frac{1}{3}\) = c\(\frac{1}{3}\) ---------(i)

⇒ (a\(\frac{1}{3}\))3 + (b\(\frac{1}{3}\))3 = (-c\(\frac{1}{3}\))3

⇒ a + b + 3.a\(\frac{1}{3}\).b\(\frac{1}{3}\)( a\(\frac{1}{3}\) + b\(\frac{1}{3}\)) = -c

⇒  a + b + 3.a\(\frac{1}{3}\).b\(\frac{1}{3}\)(-c)\(\frac{1}{3}\) = -c

⇒ a + b + c = 3.a\(\frac{1}{3}\).b\(\frac{1}{3}\).c\(\frac{1}{3}\)

⇒  (a + b + c)3 = (3.a\(\frac{1}{3}\).b\(\frac{1}{3}\).c\(\frac{1}{3}\))3

⇒ (a + b + c)3 = 27abc



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