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Question

If the roots of the equation c2-abx2-2a2-bcx+b2-ac=0 are equal, prove that either a = 0 or a3 + b3 + c3 = 3abc.

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Solution

The given quadric equation is, and roots are equal.

Then prove that either or

Here,

As we know that

Putting the value of

The given equation will have real roots, if

So, either

Hence


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