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In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. 6x2 – 5x + 1 = 0

II. y2 + y – 2 = 0


1. x > y
2. x < y
3. x ≥ y
4. x ≤ y
5. x = y or relation between x and y can not be established.

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Correct Answer - Option 5 : x = y or relation between x and y can not be established.

Calculation:

From I,

 6x2 – 5x + 1 = 0

⇒  6x2 – 2x – 3x + 1 = 0

⇒ 2x(3x – 1) – 1(3x – 1) = 0

⇒ (3x – 1)(2x – 1) = 0

Taking,

⇒ (3x – 1) = 0 or  (2x – 1) = 0

⇒ x = (1/3) or (1/2)

From II,

y2 + y – 2 = 0

⇒ y2 + 2y – y – 2 = 0

⇒ y(y + 2) – 1(y + 2) = 0

⇒ (y + 2)(y – 1) = 0

Taking,

⇒ (y + 2) = 0 or (y – 1) = 0

⇒ y = -2 or 1

Comparison between x and y (via Tabulation):

Value of x

Value of y

Relation

1/3

-2

x > y

1/3

1

x < y

1/2

-2

x > y

1/2

1

x < y

 

 x = y or relation between x and y can not be established.

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