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October 12th, 2007, 08:06 PM   #1
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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
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October 12th, 2007, 09:11 PM   #2
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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
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October 12th, 2007, 09:17 PM   #3
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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.
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October 15th, 2007, 06:35 AM   #4
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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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