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In the given questions, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer.

I. 6x2 + (1/2) = (7/2)x

II. 12y2 + 2 = 10y


1. x < y
2. x > y
3. No relation in x and y or x = y
4. x ≤ y
5. x ≥ y

1 Answer

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Best answer
Correct Answer - Option 4 : x ≤ y

Calculations: 

From I,

6x2 + (1/2) = (7/2)x

⇒ 12x2 - 7x+ 1 = 0

⇒ 12x2 - 4x - 3x + 1 = 0

⇒ 4x(3x - 1) - 1(3x - 1) = 0

⇒ (4x - 1)(3x - 1) = 0

Taking,

⇒ 3x - 1 = 0 or 4x - 1 = 0

⇒ x = 1/3 or x = 1/4

From II,

12y2 + 2 = 10y

12y2 - 10y + 2 = 0

⇒ 12y2 - 6y - 4y + 2 = 0

⇒ 6y(2y - 1) - 2(2y - 1) = 0

Taking,

⇒ 2y - 1 = 0 or 6y - 2 = 0

⇒ y = 1/2 or y = 1/3

Comparison between x and y (via Tabulation):

x

Y

Relation

1/3

1/2

x < y

1/3

1/3

x = y

1/4

1/2

x < y

1/4

1/3

x < y

 

​∴ x ≤ y.

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