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MCIII Algebra 3.30

 
 
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MCIII Algebra 3.30
by Tina Jin - Friday, January 12, 2024, 2:04 PM
 

Hello,

I need some help on this question. After squaring both sides, rearranging, then squaring again:

x^4-8x^2+x+12=0. 

I tried rational root, grouping, and double cross method to find the roots, but I'm not sure how to get the roots.

I also tried the "reversing role" method, by letting a=4 and trying to solve the equation for a, but I then I didn't find a way to factor it and after plugging in the quadratic formula I got a quartic again but now in terms of a and even more complicated.

Thanks,

Tina Jin

 
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Re: MCIII Algebra 3.30
by Xilong Lin - Friday, January 12, 2024, 10:14 PM
 

The left hand side is equal to ( x^2 - x - 3 ) (x^2 + x -4 ).

Picture of Tina Jin
Re: MCIII Algebra 3.30
by Tina Jin - Sunday, January 14, 2024, 8:47 AM
 

Oh I messed up on the double cross method, thank you for your response!