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Q.

Let Δ=det⁡a    b    cb    c    ac    a    b . Then which of the following statements is false for a,b,c∈R ?

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a

Δ>0   if  a=−1,  b=−2,  c=−3

b

Δ<0   if  a=1,  b=2,  c=3

c

Δ=0 if and only if a=b=c

d

Δ=0 if and only if a3+b3+c3=3abc

answer is C.

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Detailed Solution

Δ=−a3+b3+c3−3abc=−12(a+b+c)(a−b)2+(b−c)2+(c−a)2
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