| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and given answer. |
| I. \[{{x}^{2}}-72=x\] |
| II. \[{{y}^{2}}=64\] |
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: B
Solution :
| I. \[{{x}^{2}}-x-72=0\] |
| \[\Rightarrow \]\[{{x}^{2}}-9x+8x-72=0\]\[\Rightarrow \]\[x\,\,(x-9)+8\,\,(x-9=0\] |
| \[\Rightarrow \]\[(x+8)(x-9)=0\]\[\Rightarrow \]\[x=9,\]\[-\,\,8\] |
| II. \[{{y}^{2}}=64\]\[\Rightarrow \]\[y=\sqrt{64}\] |
| \[\therefore \] \[y=\pm \,\,8\] |
| Hence, \[x\ge y\] |
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