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The solutions of x(2x-7)=3 may be expressed in the form $\frac{m+\sqrt{n}}{p}$ and $\frac{m-\sqrt{n}}{p}$, where m, n, and p are relatively prime numbers. Find m+n+p.

Thanks!

 Jun 9, 2019
 #1
avatar+102937 
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x(2x - 7) = 3  simplify

 

2x^2 - 7x - 3  = 0

 

2 ( x^2 - (7/2)x - 3/2)  = 0     divide through by 2

 

x^2 - (7/2)x - 3/2   = 0      complete the square on x

 

x^2 - (7/2)x  = 3/2

 

x^2 - (7/2)x  + 49/16   =  3/2 + 49/16

 

(x - 7/4)^2  =  (24 + 49) / 16

 

( x - 7/4)^2 = ( 73) / 16           take both roots

 

x - 7/4  =  ±√(73) / 4

 

x =   [ 7 ±√(73)  ] / 4

 

m = 7   n = 73   and p =4

 

So    m + n + p  =   84

 

 

cool cool cool

 Jun 9, 2019

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