# In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer. I. 3x2 – 4x - 32 = 0 II. 7

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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. 3x2 – 4x - 32 = 0

II. 7y2 – 8y - 12 = 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.

Given:

I. 3x2 – 4x - 32 = 0

II. 7y2 – 8y - 12 = 0

Calculation:

From I,

3x2 – 4x - 32 = 0

⇒ 3x2 – 12x + 8x - 32 = 0

⇒ 3x(x - 4) + 8(x - 4) = 0

⇒ (x - 4)(3x + 8) = 0

Taking,

⇒ (x - 4) = 0 or  (3x + 8) = 0

⇒ x = 4 or (-8/3)

From II,

II. 7y2 – 8y - 12 = 0

⇒ 7y2 – 14y + 6y - 12 = 0

⇒ 7y(y - 2) + 6(y - 2) = 0

⇒ (y - 2)(7y + 6) = 0

Taking,

⇒ (y - 2) = 0 or (7y + 6) = 0

⇒ y = 2 or (-6/7)

Comparison between x and y (via Tabulation):

 Value of x Value of y Relation 4 2 x > y 4 -6/7 x > y -8/3 2 x < y -8/3 -6/7 x < y

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