| Directions: In the following questions, two equations I and II are given. You have to solve both the equation and give answer. |
| I. \[5{{x}^{2}}-18x+9=0\] |
| II. \[3{{y}^{2}}+5y-2=0\] |
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. \[5{{x}^{2}}-18x+9=0\] |
| \[\Rightarrow \]\[5{{x}^{2}}-15x-3x+9=0\] |
| \[\Rightarrow \]\[5x\,\,(x-3)-3\,\,(x-3)=0\] |
| \[\Rightarrow \] \[(5x-3)(x-3)=0\] |
| \[\Rightarrow \] \[x=3,\]\[\frac{3}{5}\] |
| II. \[3{{y}^{2}}+5y-2=0\] |
| \[\Rightarrow \]\[3{{y}^{2}}+6y-y-2=0\] |
| \[\Rightarrow \]\[3y\,\,(y+2)-1\,\,(y+2)=0\] |
| \[\Rightarrow \] \[(3y-1)(y+2)=0\] |
| \[\Rightarrow \] \[y=-\,\,2,\]\[\frac{1}{3}\] |
| \[\therefore \]\[y<x\] |
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