| Directions: In each of the following questions two equations are given. Solve these equations and give answer. [IBPS (SO) 2013] |
| I. \[{{x}^{2}}-6x=7\] |
| II. \[2{{y}^{2}}+13y+15=0\] |
A) If \[x<y\]
B) If \[x>y\]
C) If \[x=y\]
D) If \[x\ge y\]
E) If \[x\le y\]
Correct Answer: B
Solution :
| I. \[{{x}^{2}}-6x-7=0\] |
| \[\Rightarrow \]\[{{x}^{2}}-7x+x-7=0\] |
| \[\Rightarrow \]\[x\,\,(x-7)+1\,\,(x-7)=0\] |
| \[\therefore \]\[x=-1,\]\[7\] |
| II. \[2{{y}^{2}}+13y+15=0\] |
| \[\Rightarrow \]\[2{{y}^{2}}+10y+3y+15=0\] |
| \[\Rightarrow \]\[2y\,\,(y+5)+3\,\,(y+5)=0\]\[\Rightarrow \]\[(2y+3)(y+5)=0\] |
| \[\therefore \]\[y=-\frac{3}{2},\]\[-\,\,5\] |
| Hence, \[x>y\] |
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