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October 12th, 2007, 08:06 PM  #1 
Newbie Joined: Oct 2007 Posts: 2 Thanks: 0  Let f(x)=x^2. Find x such that f(x+1)=f(x+2).
Is there a definite value for x that will make the two equations equal one another? I cannot seem to find a value that x will equal to make the two equations equal one another. I am tempted to say that there is no value for x that will do this. I've even tried graphing the equations but I see that the lines never intersect, therefore further egging me to state that there is no value for x to make the two equations equal. I have tried to solve for x and I've done it this way: (x+1)(x+1)=x^2+x+x+2=x^2+2x+2 (x+2)(x+2)=x^2+2x+2x+4=x^2+4x+4 x^2+2x+2=x^2+4x+4 x^2 x^2 2x+2=4x+4 2 2 2x=4x+2 4x 4x 2x=2   2 2 x=1 
October 12th, 2007, 09:11 PM  #2 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
f(x+1)=(x+1)^2=f(x+2)=(x+2)^2 x^2+2x+1=x^2+4x+4 2x=3 x=3/2 
October 12th, 2007, 09:17 PM  #3 
Senior Member Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus 
f(x+1)=f(x+2) (x+1)^2=(x+2)^2 What you did wrong was the expansion of (x+1)^2. It's actually x^2+2x+1, not x^2+2x+2. Your method will solve for the solution, x=3/2. No complex solutions. 
October 15th, 2007, 06:35 AM  #4 
Newbie Joined: Oct 2007 Posts: 2 Thanks: 0  thank you!
thank you both so much for your help! i cannot believe I made this kind of mistake! something so simple turned out to be a weekend's nightmare! but thank you both for waking me up! 

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