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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. 2x2 - (4 + √13)x + 2√13 = 0

II. 10y2 - (18 + 5√13)y + 9√13 = 0


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

1 Answer

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Best answer
Correct Answer - Option 3 : x ≥ y

Calculations: 

From I,

2x2 - (4 + √13)x + 2√13 = 0

⇒ 2x2 - 4x - √13x + 2√13 = 0

⇒ 2x(x - 2) - √13(x - 2) = 0

⇒ (2x - √13)(x - 2) = 0

Taking,

⇒ 2x - √13 = 0 or x - 2 = 0

⇒ x = √13/2 or x = 2

From II,

10y2 - (18 + 5√13)y + 9√13 = 0

⇒ 10y2 - 18y - 5√13y + 9√13 = 0

⇒ 2y(5y - 9) - √13(5y - 9) = 0

⇒ (5y - 9)(2y - √13) = 0

Taking,

⇒ 5y - 9 = 0 or 2y - √13 = 0

⇒ y = 9/5 or y = √13/2

Comparison between x and y (via Tabulation):

x

Y

Relation

√13/2

9/5

x = y

√13/2

√13/2

x = y

2

9/5

x > y

2

√13/2

x > y


∴ After comparing x and y both, x ≥ y.

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