Given that their are 3 positive real numbers $a,b,c$, such that $a^2+b^2+c^2=3$, find the minimum value of $a+b+c$
2025-01-13 02:38:59.1736735939
If $a^2+b^2+c^2 =3$, find the minimum value of $a+b+c$
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$(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)$ seeking the minimum in nonnegative variables you minimize $(ab+bc+ac)$ for it is zero having two null variables example $a=b=0.$ Finally the minimum is $a+b+c=\sqrt{3}$.