Solution 2.3:10b
From Förberedande kurs i matematik 1
The inequality 1−x2
2y−3
x
2+3
2
2+3
2
The region y ≤ 1 - x² | The region x ≥ 2y - 3 |
Of the figures above, it seems that the region associated with the parabola lies completely under the line 2+3
2
The region y ≤ 1 - x² and x ≥ 2y - 3 |
Note: If you feel unsure about whether the parabola really does lie under the line, i.e. that it just happens to look as though it does, we can investigate if the y-values on the line 2+3
2
|
If this difference is positive regardless of how x is chosen, then we know that the line's y-value is always greater than the parabola's y-value. After a little simplification and completing the square, we have
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and this expression is always positive because x+41
2