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Find all values of x such that 6x = 35/x - 42/x^2. If you find more than one value, then list your solutions in increasing order, separated by commas.

 Dec 30, 2020
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6x = 35/x  - 42x^2        multiply through  by   x^2

 

6x^3  = 35x  - 42         rearrange  as

 

6x^3  - 35x  +  42    =  0     

 

This  only  has one real  solution    x  ≈ -2.8754

 

The  complex solutions are

 

x ≈  1.4377  - .6062 i      and      x ≈   1.4377 + .6062 i

 

 

cool cool cool

 Dec 30, 2020

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