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The solutions of x(2x-7)=8 may be expressed in the form (m + sqrt(n))/p and (m - sqrt(n))/p, where m, n, and p are relatively prime numbers. Find m+n+p.

 Aug 10, 2021
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x(2x-7)=8

2x^2 - 7x = 8

2x^2 - 7x - 8 = 0

 

Using the quadratic formula \(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) 

 

\(\frac{7 \pm \sqrt{49+64}}{4}\) 

\(\frac{7 \pm \sqrt{113}}{4}\) 

\(\frac{7 + \sqrt{113}}{4}\) and \(\frac{7 - \sqrt{113}}{4}\) 

So m = 7 n = 113 p = 4

7 + 113 + 4 = \(\boxed{124} \)

 Aug 10, 2021

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