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Find the difference of maximum and minimum values of x^+4x+9 / x^2 +9

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Solution:  

          \ \ Rightarrow hspace1cm y=fracx^2+4x+9x^2+9\ \ Rightarrow hspace1cm(y-1)x^2-4x+9(y-1)=0\ \ Rightarrow hspace1cmDgeq0Rightarrow 16-36(y-1)^2geq0\ \ Rightarrow hspace1cm4-9(y-1)^2geq0\ \ Rightarrow hspace1cmfrac13leq yleq frac53

     herefore     Difference of maximum and minimum values is   

                         frac53-frac13=frac43

Posted by

Deependra Verma

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