    Question

# If x=a+b, y=α x+bβ and z=aβ+bα, where α and β are complex cube roots of unty,then xyz=

A
a2 + b2
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B
a3 + b3
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C
a3 b3
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D
a3 - b3
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Solution

## The correct option is B a3 + b3CONVENTIONAL APPROACH: If x=a+by=aα+bβ and z=αβ+βα Then xyz=(a+b)(aw+bw2)(aw2+bw),where α=w and β=w2 =(a+b)(a2+abw2+abw+b2) =(a+b)(a2−ab+b2)=a3+b3 This is a variable to variable question i.e. the question is invariables and the options are in variables.So, we can assume and substitute any value for the variables. Tricks: Put a=b=2 Then x=4,y=2(w+w2)=−2 and z=2(w2+w)=−2 ∵ xyz=4(−2)(−2)=16 and (b) i.e. a3+b3=16. This method works on elimination. (B) is the correct option because (A), (B) and (D) are not equal to 16.  Suggest Corrections  0      Similar questions  Related Videos   Properties
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