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Question Number 137597 by bemath last updated on 04/Apr/21

$$$$ Find the minimum value of x^(2) +y^(2) +z^(2) , subject to the condition 2x+3y+5z=30? \n

Answered by EDWIN88 last updated on 04/Apr/21

Answered by mr W last updated on 04/Apr/21

$$x^2+y^2+z^{2}isthesquareddistance$$ $$frompoint(x,y,z)totheorgin.so$$ $$theminimumof{x}^2+y^2+z^{2}isthe$$ $$squareddistancefromorigintothe$$ $$plane2x+3y+5z-30=0.thatis$$ $${\left(\frac{-30}{\sqrt{2^2+3^2+5^2}}\right)}^2=\frac{450}{19}$$

Commented byotchereabdullai@gmail.com last updated on 04/Apr/21

$$\mathrm{nice}\mathrm{shortcut}$$

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