Let x&y be real numbers such that : $\displaystyle -2 \leq x \leq 1$ and $\displaystyle 1 \leq 3x-x^2+2y^2 \leq 22 $

Show that : $\displaystyle -4 \leq y \leq 4$

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- May 26th 2011, 01:12 PMTWiXInequalities. (1)
Let x&y be real numbers such that : $\displaystyle -2 \leq x \leq 1$ and $\displaystyle 1 \leq 3x-x^2+2y^2 \leq 22 $

Show that : $\displaystyle -4 \leq y \leq 4$ - May 26th 2011, 01:17 PMAckbeet
I would start by letting $\displaystyle f(x)=3x-x^{2},$ and finding its extremes on the interval $\displaystyle [-2,1].$ What do you get?

- May 26th 2011, 01:26 PMTWiX
Finding extremes is a method in calculus.

This is pre-calculus subforum. - May 26th 2011, 01:29 PMAlso sprach Zarathustra
-2<x<1

-6<3x<3

0<x^2<1

-6<3x-x^2<2 - May 26th 2011, 03:46 PMLoblawsLawBlog
- May 26th 2011, 04:42 PMAckbeet