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Least value of expression x2+4y2+9z2-2x+8y+27z+15 is

Srinivas , 9 Years ago
Grade 12
anser 1 Answers
jagdish singh singh

Last Activity: 9 Years ago

$\hspace{-0.7cm} Let $\bf{f(x,y) = x^2+4y^2+9z^2-2x+8y+27z+15 }$\\\\So $\bf{f(x,y) = (x-1)^2+4(y+1)^2+9\left(z+\frac{3}{2}\right)^2-\frac{41}{4}}\geq -\frac{41}{4}$\\\\ and equality hold when $\bf{x=1\;\;,y=-1\;\;,z=-\frac{3}{2}.}$

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