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Find all solutions of the equation
|x^2 - 30x - 1| + |x^2 - 30x + 29| = 30

 Mar 9, 2024
 #2
avatar+128794 
+1

abs (x)   = sqrt (x^2)

 

sqrt [ (x^2 -30x -1)^2 ]  + [sqrt [ (x^2 -30x + 29)^2 ] =  30        square both sides

 

(x^2 - 30x - 1)^2  + 2 sqrt [ (x^2 -30x -1)^2 (x^2 -30x + 29)^2] +(x^2 -30x + 29)^2 =  900

 

Solving this wouldn't be easy

 

Using a little technology  (WolframAlpha)  shows the solutions to be

 

[  -1 / (15 + sqrt (226)) , 1 ]   U  [ 29, 15 + sqrt (226 ] 

 

cool cool cool

 Mar 9, 2024

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