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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. \(6{x^2} - 7x + 2 = 0\)

II. \(2{y^2} - 5y + 3 = 0\)


1. x > y
2. x < y
3. x ≥ y
4. x ≤ y
5. x = y or relationship between x and y cannot be established

1 Answer

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Best answer
Correct Answer - Option 2 : x < y

I. \(6{x^2} - 7x + 2 = 0\)

\( \Rightarrow 6{x^2} - 3x - 4x + 2 = 0\)

\( \Rightarrow 3x\left( {2x - 1} \right) - 2\left( {2x - 1} \right) = 0\)

\( \Rightarrow \left( {2x - 1} \right)\left( {3x - 2} \right) = 0\)

\( \Rightarrow x = \frac{1}{2}\) or \(\frac{2}{3}\)

 

II. \(2{y^2} - 5y + 3 = 0\)

\( \Rightarrow 2{y^2} - 2y - 3y + 3 = 0\)

\( \Rightarrow 2y\left( {y - 1} \right) - 3\left( {y - 1} \right) = 0\)

\( \Rightarrow \left( {y - 1} \right)\left( {2y - 3} \right) = 0\)

\( \Rightarrow y = 1\) or \(\frac{3}{2}\)

Comparison between x and y (via Tabulation):

Value of x

Value of y

Relation

1/2

1

x < y

1/2

3/2

x < y

2/3

1

x < y

2/3

3/2

x < y


∴ Clearly x < y 

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