- #1
Albert1
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$a>0,b>0,c>0 ,\,\, and \,\, a+b+c=1$
find $min(\sqrt {a^2+b^2}+\sqrt {b^2+c^2}+\sqrt {c^2+a^2} )$
find $min(\sqrt {a^2+b^2}+\sqrt {b^2+c^2}+\sqrt {c^2+a^2} )$
Albert said:$a>0,b>0,c>0 ,\,\, and \,\, a+b+c=1$
find $min(\sqrt {a^2+b^2}+\sqrt {b^2+c^2}+\sqrt {c^2+a^2} )$
Albert said:$a>0,b>0,c>0 ,\,\, and \,\, a+b+c=1$
find $min(\sqrt {a^2+b^2}+\sqrt {b^2+c^2}+\sqrt {c^2+a^2} )$
The minimum value of the expression is 2, which occurs when a, b, and c are all equal to 0.5.
The minimum value can be found by setting a, b, and c to be equal to each other and solving for the value that makes the expression equal to 2.
No, the minimum value of the expression cannot be negative. This can be seen by considering the individual terms, which are all square roots of positive numbers.
No, the minimum value of the expression cannot be greater than 2. This can be seen by considering the individual terms, which are all square roots of numbers less than or equal to 1.
No, there are no other values of a, b, and c that give the minimum value of 2. This can be seen by graphing the expression and observing that the minimum occurs only at (0.5, 0.5, 0.5).