Question

Va rog . Determinati cea mai mica valoare a numarului A=RADICAL din xpatrat-10x+29+RADICAL din ypatrat+4y+5.

Answer 1

$N= \sqrt{ x^{2} -10x+29}+ \sqrt{ y^{2} +4y+5}= \\ ~'~~= \sqrt{ x^{2} -10x+25+4}+ \sqrt{ y^{2}+4y+4+1 }= \\ ~'~~= \sqrt{(x-5)^{2}+4} + \sqrt{(y+2)^2+1}. \\ \\ N=minim~daca~ (x-5)^2=minim~si~(y+2)^{2}=minim. \\ min~(x-5)^2=0~(pentru~x=5) \\ min~(y+2)^2=0~(pentru~y=-2) \\ \\ min~N= \sqrt{4}+ \sqrt{1}= 2+1=3. \\ \\ Minimul~se~obtine~pentru~x=5~si~y=-2.$