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Question

Prove that both the roots of the equation x-a x-b+x-b x-c+x-c x-a=0 are real but they are equal only when a = b = c.

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Solution

The quadric equation is

Here,

After simplifying the equation

As we know that

Putting the value of

Since, . So the solutions are real

Let

Then

Thus, the value of

Therefore, the roots of the given equation are real and but they are equal only when,

Hence proved


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