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June 11th, 2015, 03:14 PM  #1 
Senior Member Joined: Jan 2015 From: USA Posts: 107 Thanks: 2  Simultaneous very hard problem
Can someone help me solve this simultaneous equation? We are to find a and b so that the three equations have a solution in common. Thanx! 
June 11th, 2015, 04:48 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,635 Thanks: 2620 Math Focus: Mainly analysis and algebra 
By writing $a$ and $b$ in terms of $x$ using the first two equations, you can find an equation (or a pair of equations) that give three possible values of $x$. You can use these values in the first two equations to find $a$ and $b$. My solutions are $(a,b) \in \big\{(0,0), (3,4), (0,2)\big\}$ 
June 11th, 2015, 07:59 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,469 Thanks: 2038 
Adding the first and third equations gives 2x² + (b  2)x = 0, so x = 0 or 1  b/2. x = 0 implies a = b = 0. x = 1  b/2 implies 1  b + b²/4  3 + 3b/2  b = 0, i.e. (b  4)(b + 2)/4 = 0. It's easy to finish from there. 
June 13th, 2015, 08:15 PM  #4 
Senior Member Joined: May 2015 From: Varanasi Posts: 110 Thanks: 5 Math Focus: Calculus 
I dont see there is a very big problem in that, there are 3 unknowns and 3 equations though it will need some manipulation.You must write your attempt.

June 14th, 2015, 04:49 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,290 Thanks: 1023  

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