JEE Advanced Mathematics question

Let , and are the AM, GM and HM respectively of two unequal positive integers. Then the equation has

Answer: (B),(C)

Solution

For unequal positive numbers and . Let be the roots:

α+β=(0,1), αβ=-(-1,0).

Since the product is negative, the roots are real, one positive () and one negative (). Explicitly, using ,

x={2

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Question ID VK-108004