if a+2b+3c=0 show that we+8b3+37c3=18abc
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If a+2b+3c=0
prove that a cube +8b cube + 27 c cube = 18abc
Solution: a+2b+3c = 0
a+2b= -3c
(a+2b)^3 = (-3c)^3
a cube + 8b cube + 2(a)(2b)(a+2b)= -27c cube
a cube + 8b cube + 2(a)(2b)(-3c)= -27c cube
a cube + 8b cube - 18abc= -27c cube
a cube + 8b cube +27c cube = 18abc
Hence proved
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