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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 - 23x + 20 = 0

II. y2 - 5y + 4 = 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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Best answer
Correct Answer - Option 5 : x = y or relation between x and y can not be established.

Given:

I. 6x2 - 23x + 20 = 0

II. y2 - 5y + 4 = 0

Calculation:

From I,

6x2 - 23x + 20 = 0

⇒ 6x2 - 15x - 8x + 20 = 0

⇒ 3x(2x - 5) - 4(2x - 5) = 0

⇒ (2x - 5)(3x - 4) = 0

Taking,

⇒ (2x - 5) = 0 or (3x - 4) = 0

⇒ x = (5/2) or (4/3)

From II,

y2 - 5y + 4 = 0

⇒ y2 - 4y - y + 4 = 0

⇒ y(y - 4) - 1(y - 4) = 0

⇒ (y - 4)(y - 1) = 0

Taking,

⇒ (y - 4) = 0 or (y - 1) = 0

⇒ y = 4 or 1

Comparison between x and y (via Tabulation):

Value of x

Value of y

Relation

5/2

4

x < y

5/2

1

x > y

4/3

4

x < y

4/3

1

x > y

 

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

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