# In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer. I. ${x^2} - 22x + 117 = 0 0 votes 9 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. \({x^2} - 22x + 117 = 0$

II. ${y^2} + 4y - 96 = 0$

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 1 : x > y

I. ${x^2} - 22x + 117 = 0$

$\Rightarrow {x^2} - 13x - 9x + 117 = 0$

$\Rightarrow x\left( {x - 13} \right) - 9\left( {x - 13} \right) = 0$

$\Rightarrow \left( {x - 13} \right)\left( {x - 9} \right) = 0$

$\Rightarrow x = 9$ or 13

II. ${y^2} + 4y - 96 = 0$

$\Rightarrow {y^2} + 12y - 8y - 96 = 0$

$\Rightarrow y\left( {y + 12} \right) - 8\left( {y + 12} \right) = 0$

$\Rightarrow \left( {y - 8} \right)\left( {y + 12} \right) = 0$

$\Rightarrow y = - 12$ or 8

Comparison between x and y (via Tabulation):

 Value of x Value of y Relation 9 -12 x > y 9 8 x > y 13 -12 x > y 13 8 x > y

∴ Clearly x > y