perplexus.info :: Just Math : Rooting for Three Roots

Rooting for Three Roots (Posted on 2012-12-23)

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)

Comments: ( Back to comment list | You must be logged in to post comments.)

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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