| 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. \[4{{x}^{2}}-29x+45=0\] |
| II. \[3{{y}^{2}}-19y+28=0\] |
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: E
Solution :
| I. \[4{{x}^{2}}-29x+45=0\] |
| \[\Rightarrow \]\[4{{x}^{2}}-20x-9x+45=0\] |
| \[\Rightarrow \]\[4x\,(x-5)-9\,(x-5)=0\] |
| \[\Rightarrow \] \[(4x-9)(x-5)=0\] |
| \[\Rightarrow \] \[x=5,\]\[x=\frac{9}{4}\] |
| II. \[3{{y}^{2}}-19y+28=0\] |
| \[\Rightarrow \]\[3{{y}^{2}}-12y-7y+28=0\] |
| \[\Rightarrow \]\[3y\,(y-4)-7\,(y-4)=0\] |
| \[\Rightarrow \]\[(3y-7)(y-4)=0\]\[\Rightarrow \]\[y=4,\]\[y=\frac{7}{3}\] |
| Hence, relationship between x and y cannot be determined. |
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