Prove that `a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.`

Prove that a^(4)+b^(4)+c^(4)>abc(a+b+c), where a,b,c>0

Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positive numbers a b c=1a n dA^T A=I , then find the value of a^3+b^3+c^3dot

Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positive numbers a b c=1a n dA^T A=I , then find the value of a^3+b^3+c^3dot

Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positive numbers a b c=1a n dA^T A=I , then find the value of a^3+b^3+c^3dot

Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positive numbers a b c=1a n dA^T A=I , then find the value of a^3+b^3+c^3dot

Prove that a^4+b^4+c^4>abc(a+b+c). [a,b,c are distinct positive real number]..

In Delta A B C , prove that t a n A+t a n B+t a n Cgeq3sqrt(3),w h e r eA ,B ,C are acute angles.

Solve the equation |a-x c b c b-x a b a c-x|=0w h e r ea+b+c!=0.

If f(x)=a x^2+b x+a^2+b^2+c^2-a b-b c-c a ,w h e r ea ,b ,c are distinct reals, has imaginary roots then (a) 2(a-b)+(a-b)^2+(b-c)^2+(c-a)^2>0 (b) f(0)>0 (c) f(-1)>0 (d)f(0)<0

If f(x)=a x^2+b x+a^2+b^2+c^2-a b-b c-c a ,w h e r ea ,b ,c are distinct reals, has imaginary roots then (a) (a-b)^2+(b-c)^2+(c-a)^2>0 (b) f(0)>0 (c) f(-1)>0 (d) f(0)<0