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Solve the inequality y2 - 3y > 18

Mathematics
JAMB 1993

Solve the inequality y2 - 3y > 18

  • A. -3 < y < 6
  • B. y < -3 or y > 6
  • C. y > -3 or y > 6
  • D. y < 3 or y < 6
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Correct Answer: Option B
Explanation

y\(^2\) - 3y > 18 = y\(^2\) - 3y - 18 > 0

y\(^2\) - 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
By simply substituting the value of y into the inequality, y > -3 is invalid, and y < 6 is also invalid.

Therefore, y < - 3 or y > 6


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