| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer. [RBI (Assistant) Scale 2011] |
| I. \[{{x}^{2}}-10x+24=0\] |
| II. \[{{y}^{2}}-9y+20=0\] |
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: B
Solution :
| I. \[{{x}^{2}}-10x+24=0\] |
| \[\Rightarrow \]\[{{x}^{2}}-6x-4x+24=0\]\[\Rightarrow \]\[x\,\,(x-6)-4\,\,(x-6)=0\] |
| \[\Rightarrow \]\[(x-4)(x-6)=0\]\[\Rightarrow \]\[x=4,\]\[6\] |
| II. \[{{y}^{2}}-9y+20=0\] |
| \[\Rightarrow \]\[{{y}^{2}}-5y-4y+20=0\]\[\Rightarrow \]\[y\,\,(y-5)-4\,\,(y-5)=0\] |
| \[\Rightarrow \]\[(y-4)(y-5)=0\]\[\Rightarrow \]\[y=4,\]\[5\] |
| Hence, \[x\ge y.\] |
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