InterviewSolution
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InterviewSolution
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Solution set of `x-sqrt(1-|x|)lt0`, isA. `[-1,(-1+sqrt(5))/2)`B. `[-1,1]`C. `[-1,(-1+sqrt(5))/2]`D. `(-1,(-1+sqrt(5))/2)` |
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Answer» Correct Answer - A We have `x-sqrt(1-|x|)lt0`…i which is defined only when `1-|x|gt0` `implies|x|le1` `implies x epsilon [-1,1]` Now, from Eq. (i) we get `x lt sqrt(1-|x|)` Case I If`x ge0` i.e. `0lexle1` `x-sqrt((1-|x|))lt0` `impliesx lt sqrt((1-x))` On squaring both sides we get `x^(2)+x-1lt0` `implies(-1-sqrt(5))/2lt xlt (-1+sqrt(5))/2` But `xge0` `:.x epsilon[0,(-1+sqrt(5))/2)` Case II If `x lt 0` i.e. `-1lexlt0` `x-sqrt((1+x))lt0` `impliesx lt sqrt(1+x)` [always true] ` x epsilon [-1,0)` Combining both cases we get `x epsilon [-1,(-1=sqrt(5))/2)` |
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