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Question

If the roots of the equation (c2ab)x22(a2bc)x+b2ac=0 are equal, prove that either a=0 or a3+b3=c3=3abc

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Solution

We have, D = 4a(a3+b3+c33abc)
Since roots are equal.
D=04a(a3+b3+c33abc)=0a=0or,a3+b3+c3=3abc

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