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Question
If a+b+c=27, then what is the value of (a−7)3+(b−9)3+(c−11)3−3(a−7)(b−9)(c−11)?
If a+b+c=27, then what is the value of (a−7)3+(b−9)3+(c−11)3−3(a−7)(b−9)(c−11)?
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Solution
The correct option is A 0
(a−7)+(b−9)+(c−11)=(a+b+c−27=0
Hence
(a−7)3+(b−9)3+(c−11)3−3(a−7)(b−9)(c−11)=0
(using x3+y3+z3−3xyz=0, if x+y+z=0)
(a−7)+(b−9)+(c−11)=(a+b+c−27=0
Hence
(a−7)3+(b−9)3+(c−11)3−3(a−7)(b−9)(c−11)=0
(using x3+y3+z3−3xyz=0, if x+y+z=0)
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