If a, b, c are positive real numbers, then prove that `{(1 + a) (1 +b)(1 +c)^(7)} gt 7^(7) a^(4) b^(4) c^(4)`

If a , b , c , are positive real numbers, then prove that (2004, 4M) {(1+a)(1+b)(1+c)}^7>7^7a^4b^4c^4

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3a cdot

If a ,b , a n dc 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 three positive real numbers , then find minimum value of (a^(2)+1)/(b+c)+(b^(2)+1)/(c+a)+(c^(2)+1)/(a+b)

If 2x^3 +ax^2+ bx+ 4=0 (a and b are positive real numbers) has 3 real roots, then prove that a+ b ge 6 (2^(1/3)+ 4^(1/3))

If a,b,c are positive real numbers and 2a+b+3c=1 , then the maximum value of a^(4)b^(2)c^(2) is equal to

If a,b,c be positive real numbers and the value of theta=tan^(- 1)sqrt((a(a+b+c))/(b c))+tan^(- 1)sqrt((b(a+b+c))/(c a)) + tan^-1sqrt((c(a+b+a))/((ab)) then tan theta is equal to

If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)^2+(b+1//c)^2+(c+1//a)^2geq75//4.

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

Prove that =|1 1 1 a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)