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For a real number x, what is the greatest possible value of the expression (3x² + 9x + 17)/(3x² + 9x + 7)?

1. 1/4
2. 41
3. 1
4. 17/7

Correct answer: 41

Solution

Let t = 3x^2+9x, whose minimum is -27/4. The expression = 1 + 10/(t+7); t+7 is smallest at t = -27/4, giving t+7 = 1/4. Then the maximum value = 1 + 10/(1/4) = 1 + 40 = 41.

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