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Find all solutions of the equation$$|x^2-20x-1|=20.$$

 Jan 9, 2020
 #1
avatar+24380 
+2

Find all solutions of the equation \(|x^2-20x-1|=20\).

 

a)
\(x^2-20x-1 = 20\)

\(\begin{array}{|rcll|} \hline x^2-20x-1 &=& 20 \\ x^2-20x-21 &=& 0 \\\\ x &=& \dfrac{20\pm\sqrt{400-4(-21)} }{2} \\ x &=& \dfrac{20\pm\sqrt{484} }{2} \\ x &=& \dfrac{20\pm 22 }{2} \\ \\ x_1 &=& \dfrac{42}{2} \\ \mathbf{x_1} &=& \mathbf{21} \\\\ x_2 &=& \dfrac{-2}{2} \\ \mathbf{x_2} &=& \mathbf{-1} \\ \hline \end{array}\)

 

b)
\(x^2-20x-1 = -20\)

\(\begin{array}{|rcll|} \hline x^2-20x-1 &=& -20 \\ x^2-20x+19 &=& 0 \\\\ x &=& \dfrac{20\pm\sqrt{400-4(19)} }{2} \\ x &=& \dfrac{20\pm\sqrt{324} }{2} \\ x &=& \dfrac{20\pm 18 }{2} \\ \\ x_3 &=& \dfrac{38}{2} \\ \mathbf{x_3} &=& \mathbf{19} \\\\ x_4 &=& \dfrac{2}{2} \\ \mathbf{x_4} &=& \mathbf{1} \\ \hline \end{array}\)

 

laugh

 Jan 9, 2020
 #2
avatar+221 
+5

please get rid of your meaningless dollar signs basically you copied, in the title:)

 Jan 9, 2020

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