What a messy problem

Algebra Level 2

The right side of this equation: 8 = x 3 − 3 x 2 + 3 x − 1 8=\sqrt{x^{3}-3x^{2}+3x-1} can be rewritten as: ( x − a ) b c (x-a)^{\frac{b}{c}} . Then, 2 x + c 3 b − a \frac{2x+c}{3b-a} can be written as m n \frac{m}{n} , where m m and n n are positive coprime integers. Find m + n m+n .


The answer is 5.

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Alan Enrique Ontiveros Salazar by Alan Enrique Ontiveros S… , 22

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1 solution

Raj Gopal
Dec 22, 2014

The (x-a)^b/c is (x-1)^3/2 which is equal to 8 on simplifying we get x=5. therefore (2x+c)/(3b-a)=12/8=3/2=m/n and m+n=5.

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