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How many real solutions are there to the equation √x+5= |2x|? (Note: Both x and 5 are under the same square root symbol)

 Mar 24, 2024
edited by Arhantio  Mar 24, 2024
 #1
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Note that    l2xl  =  sqrt [ (2x)^2 ] 

 

So

 

sqrt  [x + 5] = sqrt [ (2x)^2]      which implies that

 

x + 5 = (2x)^2

 

x + 5 = 4x^2

 

4x^2  - x -  5  =  0

 

(4x - 5) ( x + 1)   = 0

 

4x  - 5  = 0             x + 1  = 0

 

x = 5/4                    x = -1

 

cool cool cool

 Mar 24, 2024

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