In each question, two equations numbered (I) and (II) are given. Solve both equations and determine the correct relationship between x and y . (I) &lt...

Question

In each question, two equations numbered (I) and (II) are given. Solve both equations and determine the correct relationship between x and y.

(I) <spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo></mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow><annotationencoding="application/xtex">9x26x+1=0</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:0.8974em;verticalalign:0.0833em;"></span><spanclass="mord">9</span><spanclass="mord"><spanclass="mordmathnormal">x</span><spanclass="msupsub"><spanclass="vlistt"><spanclass="vlistr"><spanclass="vlist"style="height:0.8141em;"><spanstyle="top:3.063em;marginright:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight">2</span></span></span></span></span></span></span></span><spanclass="mspace"style="marginright:0.2222em;"></span><spanclass="mbin"></span><spanclass="mspace"style="marginright:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;verticalalign:0.0833em;"></span><spanclass="mord">6</span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="marginright:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="marginright:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">1</span><spanclass="mspace"style="marginright:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="marginright:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">0</span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">9x^2 - 6x + 1 = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8974em;vertical-align:-0.0833em;"></span><span class="mord">9</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">6</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>

(II) <spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>36</mn><msup><mi>y</mi><mn>2</mn></msup><mo></mo><mn>12</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow><annotationencoding="application/xtex">36y212y+1=0</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:1.0085em;verticalalign:0.1944em;"></span><spanclass="mord">36</span><spanclass="mord"><spanclass="mordmathnormal"style="marginright:0.03588em;">y</span><spanclass="msupsub"><spanclass="vlistt"><spanclass="vlistr"><spanclass="vlist"style="height:0.8141em;"><spanstyle="top:3.063em;marginright:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight">2</span></span></span></span></span></span></span></span><spanclass="mspace"style="marginright:0.2222em;"></span><spanclass="mbin"></span><spanclass="mspace"style="marginright:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.8389em;verticalalign:0.1944em;"></span><spanclass="mord">12</span><spanclass="mordmathnormal"style="marginright:0.03588em;">y</span><spanclass="mspace"style="marginright:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="marginright:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">1</span><spanclass="mspace"style="marginright:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="marginright:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">0</span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>36</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">36y^2 - 12y + 1 = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0085em;vertical-align:-0.1944em;"></span><span class="mord">36</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">12</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>

Options

A.

x = y or no relation can be established

B.

x > y

C.

x < y

D.

xyx \geq y

E.

xyx \leq y

quadratic equationscomparisonalgebra

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