# 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} - 25x + 14 = 0 0 votes 14 views in Aptitude closed 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} - 25x + 14 = 0$

II. $9{y^2} - 9y + 2 = 0$

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

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Correct Answer - Option 3 : x ≥ y

I. $6{x^2} - 25x + 14 = 0$

$\Rightarrow 2x\left( {3x - 2} \right) - 7\left( {3x - 2} \right) = 0$

$\Rightarrow \left( {2x - 7} \right)\left( {3x - 2} \right) = 0$

$\Rightarrow x = \frac{7}{2}$ or $\frac{2}{3}$

II. $9{y^2} - 9y + 2 = 0$

$\Rightarrow 9{y^2} - 6y - 3y + 2 = 0$

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

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

$\Rightarrow y = \frac{1}{3}$ or $\frac{2}{3}$

Comparison between x and y (via Tabulation):

 Value of x Value of y Relation 7/2 1/3 x > y 7/2 2/3 x > y 2/3 1/3 x > y 2/3 2/3 x = y

∴ $\,x \ge y$