Directions : In these questions, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer. [NICL (AO) 2014] |
I. \[22{{x}^{2}}-x-6=0\] |
II. \[63{{y}^{2}}-11y-40=0\] |
A) If \[x\le y\]
B) lf \[x<y\]
C) If \[x>y\]
D) If relationship between x and y cannot be established
E) lf \[x\ge y\]
Correct Answer: D
Solution :
I. \[22{{x}^{2}}-x-6=0\] |
By splitting the middle term, |
\[22{{x}^{2}}+11x-12x-6=0\] |
\[11x\,(2x+1)-6\,(2x+1)=0\] |
\[(11x-6)(2x+1)=0\] |
\[x=\frac{6}{11},\]\[x=-\frac{1}{2}\] |
value of \[x=\left( \frac{6}{11},\,-\frac{1}{2} \right)\] |
II. \[63{{y}^{2}}-11y-40=0\] |
By splitting the middle term. |
\[63{{y}^{2}}+45y-56y-40=0\] |
\[9y\,(7y+5)-8\,(7y+5)=0\] |
\[(9y-8)(7y+5)=0\] |
\[y=\frac{8}{9},\]\[y=-\frac{5}{7}\] |
value of \[y=\left( \frac{8}{9},-\frac{5}{7} \right)\] |
Hence, relationship between x and y cannot be established. |
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