InterviewSolution
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InterviewSolution
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Solve the equation `x((3-x)/(x+1))+(x+(3-x)/(x+1))=2` |
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Answer» Hence `x+1!=0` and let `x((3-x)/(x+1))=u` and `x+(3-x)/(x+1)=v` `:.uv=2`……….i and `u+v=x((3-x)/(x+1))+x+((3-x)/(x+1))` `=(x+1)((3-x)/(x+1))+x=3-x+x=3` `:.u+v=3` and `uv=2` Then `u=2,v=1` or `u=1,v=2` Givnen equation is equivalent to the collection `:.{(x((3-x)/(x+1))=2),(x+(3-x)/(x+1)=1):}` or `{(x((3-x)/(x+1)))=1),(x+(3-x)/(x+1)=2):}` `implies{(x^(2)-x+2=0),(x^(2)-x+2=0):}` or `{(x^(2)-2x+1=0),(x^(2)-2x+1=0):}` `implies{(x^(2)-x+2=0),(x^(2)-2x+1=0):}implies{((x-1/2)^(2)+7/4!=0),((x-1)^(2)=0):}` `:.(x-1)^(2)=0` `impliesx=1` is a unique solution of the original equation. |
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