A) \[(0,\infty )\]
B) \[[1,\infty )\]
C) \[(-1,\infty )\]
D) \[(-1,1]\]
Correct Answer: B
Solution :
\[x+y=|a|\] \[ax-y=1\] if\[a>0\] \[x+y=a\] \[ax-y=1\] ------------------------------------- \[x(1+a)=1+a\,as\,x=1\] \[y=a-1\] It is first quadrant so \[a-1\ge 0\] \[a\ge 1\] \[a\in [1,\infty )\] If\[a<0\] \[x+y=-a\] + --------------------- \[x(1+a)=1-a\] \[x=\frac{1-a}{1+a}>0\Rightarrow \frac{a-1}{a+1}<0\] ?..(1) \[y=-a-\frac{1-a}{1+a}\] \[=\frac{-a-{{a}^{2}}-1+a}{1+a}>0\] \[\left( \frac{{{a}^{2}}+1}{a+1} \right)>0\Rightarrow \frac{{{a}^{2}}+1}{a+1}<0\] ?..(2) from (1) and (2)\[a\in \{\phi \}\] So correct answer is \[a\in [1,\infty )\]You need to login to perform this action.
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