If `a+b+c=0,a^2+b^2+c^2=4,t h e na^4+b^4+c^4` is_____.

If a + b + c = 0 and a^(2) + b^(2) + c^(3) = 4, them find the value of a^(4) + b^(4) +c^(4) .

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2, B=b^2c+b c^2-a^2b-a b^2, and C=a^2c+a c^2-b^2c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

If a^2+b^2+c^2=1,t h e na b+b c+c a lie in the interval [1/3,2] b. [-1,2] c. [-1/2,1] d. [-1,1/2,]

If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the minimum value of a+b+c is (a) 1 (b) 3 (c) 5 (d) 9

If 2sec^2A-sec^4A-2cos e c^2A+cos e c^4A=(15)/4,t h e n tan A is equal 1//sqrt(2) (b) 1/2 (c) 1/2sqrt(2) (d) -1/(sqrt(2))

In triangle, A B Cif2a^2b^2+2b^2c^2=a^4+b^4+c^4, then angle B is equal to 45^0 (b) 135^0 120^0 (d) 60^0

If c^(2) = a^(2) + b^(2) , then prove that 4s (s - a) (s - b) (s - c) = a^(2) b^(2)

Given A=|a b 2c d e 2f l m 2n|,B=|f 2d e 2n 4l 2m c 2a b| , then the value of B//A is ___________.

Given A=|a b2c d e2fl m2n|,B=|f2d e2n4l2m c2a b| , then the value of B//A is ___________.

If a gt 0 and b^(2) - 4 ac = 0 then solve ax^(3) + (a + b) x^(2) + (b + c) x + c gt 0 .