Weirdratic Function

Level 2

The equation

( x − 3 x ) 2 + ( x − 3 x ) − 6 = 0 (x - \frac{3}{x})^{2} + (x - \frac{3}{x}) - 6 = 0 ,

has roots a , b and c ± d e \frac{c \pm \sqrt{d}}{e} . Find the value of ∣ a ∣ + ∣ b ∣ + ∣ c ∣ + ∣ d ∣ + ∣ e ∣ |a| + |b| + |c| + |d| + |e| .


The answer is 30.

Mc Jason Laurete by Mc Jason Laurete , 23, Philippines

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1 solution

( x − 3 x ) = y (x-\frac{3}{x}) = y y 2 + y − 6 = 0 y^2 + y - 6 = 0 y = − 3 or 2 y = -3 \; \text{or} \; 2 x − 3 x = − 3 or x − 3 x = 2 x - \frac{3}{x} = -3 \; \text{or} \; x - \frac{3}{x} = 2 x 2 + 3 x − 3 = 0 or x 2 − 2 x − 3 = 0 x^2 +3x - 3 = 0 \; \text{or} \; x^2 -2x - 3 = 0 x = − 3 ± 21 2 or x = − 1 or 3 x = \frac{-3 \pm \sqrt{21}}{2} \; \text{or} \; x = -1 \; \text{or} \; 3 a = − 1 , b = 3 , c = − 3 , d = 21 , e = 2 a=-1, b=3, c=-3, d=21, e=2 ∣ a ∣ + ∣ b ∣ + ∣ c ∣ + ∣ d ∣ + ∣ e ∣ = 30. \boxed{|a|+|b|+|c|+|d|+|e|=30.}

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