x2 + x - 20 = 0y2 - y

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Direction: In each of the following question, there are two equations. you have to solve both equations and give answer.

x² + x - 20 = 0
y² - y - 30 = 0

1. If x > y
2. If x ≥ y
3. If x < y
4. If x ≤ y
5. If x = y or relation cannot be established

Correct Option: D

x² + x - 20 = 0
[by factorisation method]
⇒ x² + 5x - 4x - 20 = 0
⇒ x(x + 5) - 4(x + 5) = 0
(x + 5) (x - 4) = 0
∴ x = -5 or 4
and y² - y - 30 = 0
⇒ y² - 6y + 5y - 30 = 0
⇒ y(y - 6) + 5(y - 6) = 0
⇒ (y - 6) (y + 5) = 0
∴ y = 6 or - 5
Hence, y ≥ x or x ≤ y