In the following question, one or two equation(s) is/are given. On their basis you have to determine the relation between x and y and then give answer
I. x2 – 6x = 7
II. 2y2 + 13y + 15 = 0
Solution
Correct Answer: Option B
Equation 1:
x2 – 6x = 7
⇒ x2 – 6x – 7= 0
⇒ x2 – 7x + x – 7= 0
⇒ x (x - 7) + 1 (x - 7) = 0
⇒ (x + 1) (x - 7) = 0
⇒ x + 1= 0 or, x – 7 = 0
⇒ x= -1 or, x = 7
Equation 2:
2y2 + 13y + 15 = 0
⇒ 2y2 + 10y + 3y + 15 = 0
⇒ 2y (y +5) + 3 (y + 5) = 0
⇒ (y + 5) (2y + 3) = 0
⇒ y + 5 = 0 or, 2y + 3= 0
⇒ y = -5 or, y = -3/2
Now comparing x and y:
x = -1 is greater than both -5 and - 3/2
x= 7 is greater than both – 5 and - 3/2
Therefore, x is greater than y
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