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The solutions of x(3x-7) = -1+4x may be expressed in the form m + sqrt n / p and m - sqrt n / p , where m, n, and p have a greatest common divisor of 1. Find m+n+p.

 Apr 16, 2022
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x (3x - 7 )   =  -1 + 4x

 

3x^2 - 7x  = -1  + 4x           simplify as

 

3x^2 - 11x + 1    = 0

 

By  the Q formula  we  haxe

 

solutions =       11 ± sqrt [ 11^2  - ( 4 * 3 * 1 ) ]                    11 ± sqrt [ 109 ]

                       _______________________  =                ______________

                                         2 * 3                                                     6

 

 

m = 11

n = 109

p = 6

 

m + n + p  =   126

 

cool cool cool

 Apr 16, 2022

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