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I've approached it a slightly different way, but I'm not entirely sure it's a solid approach.
At this point we can just ignore the modulus on the right hand side, as that expression is positive for all real x anyway.
I've then sketched the two equations, and found where they meet:
And
I've then said that, because each of the solutions to these has a double root, the graphs only touch at those points but don't cross. This therefore means that the quadratic must either be greater than or equal to |2x+2|.
Is this sufficient?
Thanks.
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NB: The graph youre asked to draw is the curve
shifted one unit to the left.Last edited by JaneFairfax (2008-06-07 03:14:43)
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edit: about your siolution, instead of setting equality between the two functions to see where they meet, keep the inequality sign and consider the same two cases.
Last edited by Kurre (2008-06-07 05:52:36)
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Why, of course! I should have known that the AMGM inequality for two variables is equivalent to (√a−√b)[sup]2[/sup] ≥ 0. Why did I have to do it the long way?
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Thanks both of you.
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