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(D) For equation $I$: $18x^2 - 13\sqrt{7}x + 14 = 0$.Splitting the middle term: $18x^2 - 9\sqrt{7}x - 4\sqrt{7}x + 14 = 0$.$9x(2x - \sqrt{7}) - 2\sqrt

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if $x = y$ or relationship between $x$ and $y$ cannot be established.

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(D) For equation $I$: $18x^2 - 13\sqrt{7}x + 14 = 0$.Splitting the middle term: $18x^2 - 9\sqrt{7}x - 4\sqrt{7}x + 14 = 0$.$9x(2x - \sqrt{7}) - 2\sqrt{7}(2x - \sqrt{7}) = 0$.$(9x - 2\sqrt{7})(2x - \sqrt{7}) = 0$.So,$x = \frac{2\sqrt{7}}{9} \approx 0.588$ and $x = \frac{\sqrt{7}}{2} \approx 1.323$.For equation $II$: $32y^2 - 19\sqrt{6}y + 9 = 0$.Splitting the middle term: $32y^2 - 16\sqrt{6}y - 3\sqrt{6}y + 9 = 0$.$16y(2y - \sqrt{6}) - 3\sqrt{2}(\sqrt{2}y - \sqrt{3}) = 0$ (or using quadratic formula).Using $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:$y = \frac{19\sqrt{6} \pm \sqrt{(19\sqrt{6})^2 - 4(32)(9)}}{2(32)} = \frac{19\sqrt{6} \pm \sqrt{2166 - 1152}}{64} = \frac{19\sqrt{6} \pm \sqrt{1014}}{64}$.$y \approx \frac{46.53 \pm 31.84}{64}$.$y_1 \approx 1.22$ and $y_2 \approx 0.23$.Comparing the values of $x$ and $y$,the relationship cannot be established.

Solve the given two equations and select the correct answer from the given options.
$I.$ $18x^2 - 13\sqrt{7}x + 14 = 0$
$II.$ $32y^2 - 19\sqrt{6}y + 9 = 0$

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Solve the given two equations and select the correct answer from the given options.$I.$ $18x^2 - 13\sqrt{7}x + 14 = 0$$II.$ $32y^2 - 19\sqrt{6}y + 9 = 0$