| Directions: In the following questions, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer. |
| I. \[3{{x}^{2}}-17x+22=0\] |
| II. \[5{{y}^{2}}-21y+22=0\] |
A) If \[x\ge y\]
B) If \[x\le y\]
C) If \[x>y\]
D) If \[x<y\]
E) If relationship between x and y cannot be established
Correct Answer: A
Solution :
| I. \[3{{x}^{2}}-17x+22=0\] |
| \[\Rightarrow \] \[3{{x}^{2}}-6x-11x+22=0\] |
| \[\Rightarrow \] \[3x\,(x-2)-11\,(x-2)=0\] |
| \[\Rightarrow \] \[x=\frac{11}{3},\] 2 |
| II. \[5{{y}^{2}}-21y+22=0\] |
| \[\Rightarrow \]\[5{{y}^{2}}-10y-11y+22=0\] |
| \[\Rightarrow \] \[5y\,(y-2)-11\,(y-2)=0\] |
| \[\Rightarrow \] \[y=\frac{11}{5},\]2 |
| \[\therefore \] \[x\ge y\] |
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