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  • The quadratic equation whose roots are minimum value of sin^2 theta -sin theta +1/2 and lim square root (x+1)(x+2) -x is As x-->infinity

The quadratic equation whose roots are minimum value of sin^2 theta -sin theta +1/2 and lim square root (x+1)(x+2) -x is As x-->infinity

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Solution:   We have ,

         sin^2 heta -sin heta+frac12   and lim_x o infty sqrt(x+1)(x+2)-x

 \ \ Rightarrow E=sin^2 heta-sin heta+frac12=(sin heta-frac12)^2+frac14

Rightarrow    Minimum value is frac14.

Let      K=sqrt(x+1)(x+2),  then 

                  K-x=fracK^2-x^2K+x=frac3x+2K+x

                  lim_x o infty(K-x)=lim_x o inftyfrac3+frac2xfracKx+1=frac32, herefore lim_x o inftyfracKx=1

Hence , The required equation is x^2-frac74x+frac38=0Rightarrow 8x^2-14x+3=0

 

 

Posted by

Deependra Verma

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