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


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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?
	Answered by EDWIN88 last updated on 04/Apr/21

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

	$x^{2} + y^{2} + z^{2} i s t h e s q u a r e d d i s t a n c e$ $f r o m p o i n t (x, y, z) t o t h e o r g i n . s o$ $t h e m i n i m u m o f x^{2} + y^{2} + z^{2} i s t h e$ $s q u a r e d d i s t a n c e f r o m o r i g i n t o t h e$ $p l a n e 2 x + 3 y + 5 z - 30 = 0 . t h a t i s$ ${(\frac{- 30}{\sqrt{2^{2} + 3^{2} + 5^{2}}})}^{2} = \frac{450}{19}$
	Commented by otchereabdullai@gmail.com last updated on 04/Apr/21

	$nice shortcut$
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