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junior college 1 | H2 Maths
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Date Posted: 4 years ago
Views: 275
(x² + x + 3)(1 - x)/(x² - 4) ≤ 0
(x² + 2(½)x + (½)² - (½)² + 3)(1 - x)/[(x + 2)(x - 2)] ≤ 0
((x + ½)² + 2¾)(1 - x)/[(x + 2)(x - 2)] ≤ 0
Now (x + ½)² ≥ 0 for all real x.
Then (x + ½)² + 2¾ > 0 for all real x.
So,
(1 - x)/[(x + 2)(x - 2)] ≤ 0 in order for (x² + x + 3)(1 - x)/(x² - 4) to be ≤ 0
If you draw the number line and test the sign of the expression at the left and right of the x = -2 , = 1 and x = 2,
The result is : -2 < x ≤ 1 or x > 2
(x² + 2(½)x + (½)² - (½)² + 3)(1 - x)/[(x + 2)(x - 2)] ≤ 0
((x + ½)² + 2¾)(1 - x)/[(x + 2)(x - 2)] ≤ 0
Now (x + ½)² ≥ 0 for all real x.
Then (x + ½)² + 2¾ > 0 for all real x.
So,
(1 - x)/[(x + 2)(x - 2)] ≤ 0 in order for (x² + x + 3)(1 - x)/(x² - 4) to be ≤ 0
If you draw the number line and test the sign of the expression at the left and right of the x = -2 , = 1 and x = 2,
The result is : -2 < x ≤ 1 or x > 2
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Date Posted:
4 years ago
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