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January 5th, 2014, 02:31 PM  #1 
Newbie Joined: Jan 2014 Posts: 6 Thanks: 0  How to solve these problems algebraically?
3x^2 + 192 = 0 x^3 + 125 = 0 I don't know where to begin for the first problem. I assumed it would be factoring a sum of squares but 192 is not a square. For the second one I am guessing it is a sum of cubes problem? Second one I got (x + 5)(x^2  5x + 25). Would I need to find the zeros and how would I do that? Not sure what it means to "solve" algebraically. 
January 5th, 2014, 02:46 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,947 Thanks: 1139 Math Focus: Elementary mathematics and beyond  Re: How to solve these problems algebraically?
1. You can't factor a sum of squares with real numbers. Otherwise, 3x² + 192 = 3(x² + 64) = 3(x  8i)(x + 8i), hence the roots are 8i and 8i. 2. x³ + 125 = (x + 5)(x²  5x + 25) = 0 implies x = 5 is a solution. Can you find x if x²  5x + 25 = 0? 
January 5th, 2014, 03:50 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: How to solve these problems algebraically? Hello, GrannySmith! Quote: Quote:  

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