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(D) For equation $I$: $63x - 194\sqrt{x} + 143 = 0$. Let $\sqrt{x} = u$. Then $63u^2 - 194u + 143 = 0$.Splitting the middle term: $63 	imes 143 = 900

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

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(D) For equation $I$: $63x - 194\sqrt{x} + 143 = 0$. Let $\sqrt{x} = u$. Then $63u^2 - 194u + 143 = 0$.Splitting the middle term: $63 	imes 143 = 9009$. We need factors of $9009$ that sum to $194$. These are $117$ and $77$.$63u^2 - 117u - 77u + 143 = 0 \Rightarrow 9u(7u - 13) - 11(7u - 13) = 0$.$(9u - 11)(7u - 13) = 0$. So,$u = 11/9$ or $u = 13/7$.$x_1 = (13/7)^2 = 169/49 \approx 3.45$ and $x_2 = (11/9)^2 = 121/81 \approx 1.49$.For equation $II$: $99y - 255\sqrt{y} + 150 = 0$. Let $\sqrt{y} = v$. Then $99v^2 - 255v + 150 = 0$. Dividing by $3$: $33v^2 - 85v + 50 = 0$.Splitting the middle term: $33 	imes 50 = 1650$. Factors are $55$ and $30$.$33v^2 - 55v - 30v + 50 = 0 \Rightarrow 11v(3v - 5) - 10(3v - 5) = 0$.$(11v - 10)(3v - 5) = 0$. So,$v = 10/11$ or $v = 5/3$.$y_1 = (10/11)^2 = 100/121 \approx 0.83$ and $y_2 = (5/3)^2 = 25/9 \approx 2.78$.Comparing values: $x_1 \approx 3.45, x_2 \approx 1.49$ and $y_1 \approx 0.83, y_2 \approx 2.78$.Since $x_1 > y_2$ but $x_2 < y_2$,the relationship cannot be established.

Solve the given two equations and select the correct answer from the given options.
$I.$ $63x - 194\sqrt{x} + 143 = 0$
$II.$ $99y - 255\sqrt{y} + 150 = 0$

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Solve the given two equations and select the correct answer from the given options.$I.$ $63x - 194\sqrt{x} + 143 = 0$$II.$ $99y - 255\sqrt{y} + 150 = 0$