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KVPY Sample Paper KVPY Stream-SX Model Paper-1

  • question_answer
    The least value of the expression \[{{x}^{2}}+4{{y}^{2}}+3{{z}^{2}}-2x-12y-6z+14\] is

    A) 0                                 

    B) 1

    C) No least value   

    D) none of these

    Correct Answer: B

    Solution :

    (b)
    let \[f\left( x,y,z \right)={{x}^{2}}+4{{y}^{2}}+3{{z}^{2}}-2x-12y-6z+14\] \[={{\left( x-1 \right)}^{2}}+{{\left( 2y-3 \right)}^{2}}+3{{\left( z-1 \right)}^{2}}+1\]
    For least value of \[f\left( x,y,z \right)\]
    \[x-1=0;2y-3=0\,\operatorname{and}\,z-1=0\]
    \[\therefore x=1;y=\frac{3}{2};z=1\]
    Hence, least value of \[f\left( x,y,z \right)\operatorname{is}\,f\left( 1,\frac{3}{2},1 \right)=1\].


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