| Directions: In the given questions, two equations numbered I and II are given. Solve both the equations and mark the appropriate answer. |
| I. \[3{{x}^{2}}-22x+7=0\] |
| II. \[{{y}^{2}}-20y+91=0\] |
A) \[x>y\]
B) \[x\ge y\]
C) \[x<y\]
D) \[x\le y\]
E) Relationship between x and y cannot be determined
Correct Answer: D
Solution :
| I. \[3{{x}^{2}}-22x+7=0\] |
| \[\Rightarrow \] \[3{{x}^{2}}-x-21x+7=0\] |
| \[\Rightarrow \] \[x\,(3x-1)-7\,(3x-1)=0\] |
| \[\Rightarrow \] \[(3x-1)(x-7)=0\]\[\Rightarrow \]\[x=\frac{1}{3},\]7 |
| II. \[{{y}^{2}}-20y+91=0\] |
| \[\Rightarrow \] \[{{y}^{2}}-7y+13y+91=0\] |
| \[\Rightarrow \] \[y\,(y-7)-13\,(y-7)=0\] |
| \[\Rightarrow \] \[(y-13)(y-7)=0\]\[\Rightarrow \]\[y=13,\]7 |
| \[\therefore \] \[y\ge x\] |
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