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Question Number 28198 by NECx last updated on 21/Jan/18
Find the shortest distance from  the origin to the curve xy=3
Findtheshortestdistancefromtheorigintothecurvexy=3
Answered by mrW2 last updated on 22/Jan/18
distance of point (x,y) to the origin is r.  r^2 =x^2 +y^2   xy=3  ⇒r^2 =x^2 +(9/x^2 )≥2(√(x^2 ×(9/x^2 )))=6    (AM≥GM)  ⇒r_(min) =(√6)
distanceofpoint(x,y)totheoriginisr.r2=x2+y2xy=3r2=x2+9x22x2×9x2=6(AMGM)rmin=6
Commented by math solver last updated on 22/Jan/18
nice !
nice!

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