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# algebra

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The solutions of  x(3x-7) = -1 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.

May 20, 2021

#1
+483
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$3x^2 - 7x = -1$

$3x^2 - 7x + 1 = 0$

$x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 1 \cdot 3}}{2 \cdot 3} = \frac{7 \pm \sqrt{37}}{6}.$

$7+37+6 = \boxed{50}$

- Jimmy

May 20, 2021

#1
+483
+1

$3x^2 - 7x = -1$

$3x^2 - 7x + 1 = 0$

$x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 1 \cdot 3}}{2 \cdot 3} = \frac{7 \pm \sqrt{37}}{6}.$

$7+37+6 = \boxed{50}$

- Jimmy

MathProblemSolver101 May 20, 2021