If , and are real numbers in the interval , what is the maximum value of the expression above to 2 decimal places?
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Since a , b , c are in the interval [ 0 , 1 ] then the supremum or the least upper bound is a number s where every element in the interval [ 0 , 1 ] should be less than s . Thus, the upper bound is 2
If we consider S as the perimeter of a triangle, then S = a + b + c .
We know that the sum of two sides is greater than half the perimeter which is 2 S ⟹
2 ( a + b ) > S
2 ( c + a ) > S
2 ( c + b ) > S
⟹ b + c a + a + c b + a + b c + ( a + b + c ) 2 ( a + b + c ) = 2