| Directions: In, each of the following questions two equations are given. You have to solve both the equations and find out values of x, y and give answer. |
| I.\[2{{x}^{2}}-13x+21=0\] |
| II. \[5{{y}^{2}}-22y+21=0\] |
A) If \[x>y\]
B) If \[x\le y\]
C) If \[x<y\]
D) If \[x\ge y\]
E) If relationship between x and y cannot be determined
Correct Answer: D
Solution :
| I. \[2{{x}^{2}}-13x+21=0\] |
| \[\Rightarrow \]\[2{{x}^{2}}-6x-7x+21=0\] |
| \[\Rightarrow \]\[2x\,(x-3)-7\,(x-3)=0\] |
| \[\Rightarrow \]\[(x-3)(2x-7)=0\]\[\Rightarrow \]\[x=3,\]\[x=\frac{7}{2}\] |
| II. \[5{{y}^{2}}-22y+21=0\] |
| \[\Rightarrow \]\[5{{y}^{2}}-15y-7y+21=0\] |
| \[\Rightarrow \]\[5y\,(y-3)-7\,(y-3)=0\] |
| \[\Rightarrow \] \[(5y-7)(y-3)=0\]\[\Rightarrow \]\[y=3,\]\[y=\frac{7}{5}\] |
| \[\therefore \] \[x\ge y\] |
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