Given are positive rational numbers `a ,b , c` such that `a+b+c=1,` then prove that `a^a b^bc^c+a^bb^cc^a+a^c b^a c^blt=1.`

Given are positive rational numbers a ,b , c such that a+b+c=1 , then prove that a^a b^bc^c+a^b b^c c^a+ a^c b^a c^b<1.

Given are positive rational numbers a ,b , c such that a+b+c=1 , then prove that a^a b^bc^c+a^b b^c c^a+ a^c b^a c^b<1.

Given are positive rational numbers a,b,c such that a+b+c=1, then prove that a^(a)b^(b)c^(c)+a^(b)b^(c)c^(a)+a^(c)b^(a)c^(b)<=1

If a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2

If a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2

If a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2

If a,b,c are positive real numbers such that a+b+c=1, then prove that (a)/(b+c)+(b)/(c+a)+(c)/(a+b)>=(3)/(2)

Prove that |b+c a a b c+a b cc a+b|=4a b c

For all rational numbers a, b and c, a (b + c) = ab + bc.

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0