Solve the inequality y2 - 3y > 18
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Correct Answer: Option A
Explanation:
y2 - 3y > 18 = 3y - 18 > 0
y2 - 6y + 3y - 18 > 0 = y(y - 6) + 3 (y - 6) > 0
= (y + 3) (y - 6) > 0
Case 1 (+, +) \(\to\) (y + 3) > 0, (y - 6) > 0
= y > -3 y > 6
Case 2 (-, -) \(\to\) (y + 3) < 0, (y - 6) < 0
= y < -3, y < 6
Combining solution in case 1 and Case 2
= x < -3y < 6
= -3 < y < 6
y2 - 3y > 18 = 3y - 18 > 0
y2 - 6y + 3y - 18 > 0 = y(y - 6) + 3 (y - 6) > 0
= (y + 3) (y - 6) > 0
Case 1 (+, +) \(\to\) (y + 3) > 0, (y - 6) > 0
= y > -3 y > 6
Case 2 (-, -) \(\to\) (y + 3) < 0, (y - 6) < 0
= y < -3, y < 6
Combining solution in case 1 and Case 2
= x < -3y < 6
= -3 < y < 6