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# C1 Solving inequalities exam question - help please

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1. This question is C1 January 2006, Q10 part (d), for reference.

I got to k^(2)<12, and then k<=+/-2root3. I thought I should leave the answer as k<2root3, as k<-2root3 is inclusive in k<2root3.

The answer is -2root3<k<2root3, and I am not sure why. Could somebody explain please?

Thank you
2. Thing about the graph of , to satisfy the inequality (replacing k with x) the curve must be below the x axis so that y<0.

You cannot just square root it when there is an inequality. By your logic -10 should satisfy the inequality, but does it in reality? No.
3. It is k>-2root3 as the square of (-2root3) is 12. If we make it more negative then k^2 will be greater than 12.

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4. I loved your explanation (http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E2-12)
It is like finding the roots of X^2-12=0
Generally I try remembering that

(Original post by B_9710)
Thing about the graph of , to satisfy the inequality (replacing k with x) the curve must be below the x axis so that y<0.

You cannot just square root it when there is an inequality. By your logic -10 should satisfy the inequality, but does it in reality? No.
5. (Original post by jamb97)
...
In addition to the above, here's a pretty picture.

The two intersections of the curve and the line are at - I'm sure you can tell which is which. Now for what values of is the curve under the or less than the line?

(Original post by depymak)
To see why this is true think about since the square root is monotone increasing function then .

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