Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45° and 60° with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is $\frac{1}{\sqrt[]{x}}.$  The value of x is

<p>W_A = W_B</p><p><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>A</mi> </mrow> </msub> <mo>×</mo> <mi>d</mi> <mo>×</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>4</mn> <mn>5</mn> <mo>=</mo> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> <mo>×</mo> <mi>d</mi> <mo>×</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>6</mn> <mn>0</mn> </mrow> </math> </span> &nbsp; &nbsp;&nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815910401"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;</p><p><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mfrac> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>A</mi> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <mi>x</mi> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math> </span><br>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1815910402"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;</p><p>=&gt; x = 2</p>

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