| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer. |
| I. \[5{{x}^{2}}-18x+9=0\] |
| II. \[20{{y}^{2}}-13y+2=0\] |
A) If \[x>y\]
B) If \[x\ge y\]
C) If \[x<y\]
D) If \[x\le y\]
E) If x = y or the relationship cannot be established
Correct Answer: A
Solution :
| I. \[5{{x}^{2}}-18x+9=0\] |
| \[\Rightarrow \] \[5{{x}^{2}}-15x-3x+9=0\] |
| \[\Rightarrow \]\[5x\,(x-3)-3\,(x-3)=0\] |
| \[\Rightarrow \] \[(x-3)(5x-3)=0\] |
| \[\Rightarrow \] \[x=3,\]\[\frac{3}{5}\] |
| II. \[20{{y}^{2}}-13y+2=0\] |
| \[\Rightarrow \] \[20{{y}^{2}}-5y-8y+2=0\] |
| \[\Rightarrow \]\[5y\,(4y-1)-2\,(4y-1)=0\] |
| \[\Rightarrow \] \[(4y-1)(5y-2)=0\] |
| \[\Rightarrow \] \[y=\frac{1}{4},\]\[\frac{2}{5}\] |
| Hence, \[x>y\] |
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