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Rooting for Three Roots (Posted on 2012-12-23) Difficulty: 3 of 5
The cubic equation x3 + ax+ a = 0 has three roots x1, x2 and x3 with x1 ≤ x2 ≤ x3, where a is real and non zero, such that:

x12/ x2 + x22/ x3 + x32/ x1 = 8

Determine x1, x2 and x3

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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agree, but . . . | Comment 2 of 3 |
I agree with the solution showing that a=8.

However, the resulting equation has only one real root and two imaginary roots, which makes meaningless the condition b ≤ c ≤ d. (I also agree that subscripts aren't needed).

I wonder if the coefficient for x should be -a instead.  That wouldn't change the value of a and would make b,c,d equal -1 - sqrt(5), 2, -1 + sqrt(5).

  Posted by xdog on 2012-12-23 22:24:49
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