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# Algebra

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The solutions of x(3x-7) = 17 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 26, 2022

#1
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Expand and convert as: $$3x^2-7x-17=0$$

Using the quadratic formula, we have: $$\large {7 \pm \sqrt{7^2-4 \times -17 \times 3} \over 6}$$

This simplifies to: $$\large {{7 \pm \sqrt{253} } \over 6 }$$

Thus, the answer is: $$253 + 7 +6 = \color{brown}\boxed{266}$$

Apr 26, 2022