| Directions: In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer [IBPS RRB (Office Assistant) 2012] |
| I. \[2{{x}^{2}}-(4+\sqrt{13})\,x+2\sqrt{13}=0\] |
| II. \[10{{y}^{2}}-(18+5\sqrt{13})y+9\sqrt{13}=0\] |
A) If \[x>y\]
B) If \[x\ge y\]
C) If \[x<y\]
D) If \[x\le y\]
E) If \[x=y\]or relationship cannot be established
Correct Answer: A
Solution :
| I. \[2{{x}^{2}}-4x-\sqrt{13}x+2\sqrt{13}=0\] |
| \[\Rightarrow \]\[2x\,\,(x-2)-\sqrt{13}(x-2)=0\] |
| \[\Rightarrow \] \[(x-2)(2x-\sqrt{13})=0\] |
| \[\therefore \] \[x=2,\]\[\frac{\sqrt{13}}{2}\] |
| II. \[10{{y}^{2}}-(18y)-5\sqrt{13}y+9\sqrt{13}=0\] |
| \[\Rightarrow \]\[2y\,\,(5y-9)-\sqrt{13}\,\,(5y-9)=0\] |
| \[\Rightarrow \] \[(5y-9)(2y-\sqrt{13})=0\] |
| \[\therefore \] \[y=\frac{9}{5},\]\[y=\frac{\sqrt{3}}{2}\] |
| Hence, \[x\ge y\] |
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