A) \[|{{\alpha }^{2}}-{{\beta }^{2}}|\]
B) \[|\alpha \beta \,({{\alpha }^{2}}-{{\beta }^{2}})|\]
C) \[\left| \frac{{{\alpha }^{2}}-{{\beta }^{2}}}{\alpha \beta } \right|\]
D) \[\left| \frac{{{\alpha }^{2}}-{{\beta }^{2}}}{{{\alpha }^{2}}{{\beta }^{2}}} \right|\]
Correct Answer: A
Solution :
Since, \[SD=\sqrt{{{60}^{2}}+{{25}^{2}}}\] and \[=\sqrt{4225}=65=DP\] are the roots of \[\Delta x=(SA+AP)-SP\] \[\Rightarrow \] and \[\Delta x=(65+65)-120\] are roots of the transformed equation \[\Rightarrow \] Let \[\Delta x=10\,m\] and \[\frac{\lambda }{2}\] be roots of \[\lambda \] \[=\left( 10-\frac{\lambda }{2} \right)\] and \[=(2n)\frac{\lambda }{2}\] all roots of \[n=0,\,\,1,\,\,2,...\] Difference between roots \[10-\frac{\lambda }{2}=(2n)\frac{\lambda }{2},\,\,n=0,\,\,1,\,2,...\] \[10=(2n+1)\frac{\lambda }{2},\,n=0,\,1,\,\,2,...\] \[\Rightarrow \]c \[\lambda =\frac{20}{2n+1},\,\,n=0,\,\,1,\,\,2,...\] \[\Rightarrow \] \[\lambda =20,\,\frac{20}{3},\,\frac{20}{5},\,\frac{20}{7},...\] \[\phi \]
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