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How many real solutions are there for $x$ in the following equation: $$(x - 5x + 12)^2 + 1 = -|x|$$

Guest Dec 18, 2014

Best Answer 

 #3
avatar+86890 
+5

Here's the graph  of both sides......https://www.desmos.com/calculator/omgitpgty8

Notice that there aren't any points of intersection.......thus...no real solutions...

 

CPhill  Dec 18, 2014
 #1
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0

Someone please help me on this.

Guest Dec 18, 2014
 #2
avatar+17736 
+5

(x - 5x + 12)2 + 1  =  -|x|   ---> is equivalent to --->    (x - 5x + 12)2 + 1 + |x|  =  0  

 (x - 5x + 12)2 can never be less than 0; similarly |x| can never be less than 0; whatever the sum of these two are, when you add another +1, you must get a number which is greater than 0.

Therefore, there can be no real solutions.

geno3141  Dec 18, 2014
 #3
avatar+86890 
+5
Best Answer

Here's the graph  of both sides......https://www.desmos.com/calculator/omgitpgty8

Notice that there aren't any points of intersection.......thus...no real solutions...

 

CPhill  Dec 18, 2014

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