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^blt=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)

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

If a, b, c are positive real numbers such that a+b+c=1 , then the greatest value of (1-a)(1-b)(1-c), is

If a,b,c are positive reral numbers such that (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b), then prove that

If a,b,c are positive real numbers and sides of a triangle,then prove that (a+b+c)^(3)>=27(a+b-c)(b+c-a)(c+a-b)

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

bc - b - c - b - c c b

If a,b, and c are distinct positive real numbers such that a+b+c=1, then prove tha ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))>8

If a,b,c are positive rational numbers such that agtbgtc and the quadratic eqution (a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0 has a root of the interval (-1,0) then (A) c+alt2b (B) the roots of the equation are rational (C) the roots of are imaginary (D) none of these

If a b c are positive real numbers such that a+b+c=1 then the least value of ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c)) is