If `a^2x^4+b^2y^4=c^6,` then the maximum value of `x y` is (a)`(c^2)/(sqrt(a b))` (b) `(c^3)/(a b)` (c) `(c^3)/(sqrt(2a b))` (d) `(c^3)/(2a b)`

If a^(2)+b^(2)+c^(2)=1 where, a,b, cin R , then the maximum value of (4a-3b)^(2) + (5b-4c)^(2)+(3c-5a)^(2) is

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

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

Prove that the greatest value of x y is c^3//sqrt(2a b)dot if a^2x^4+b^4y^4=c^6dot

Prove that the minimum value of ((a+x)(b+x))/((c+x))a ,b > c ,x >-c is (sqrt(a-c)+sqrt(b-c))^2

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

Vertices of a variable acute angled triangle A B C lies on a fixed circle. Also, a ,b ,ca n dA ,B ,C are lengths of sides and angles of triangle A B C , respectively. If x_1, x_2a n dx_3 are distances of orthocenter from A ,Ba n dC , respectively, then the maximum value of ((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c)) is -sqrt(3) b. -3sqrt(3) c. sqrt(3) d. 3sqrt(3)

If a,b,c,in R^(+) , such that a+b+c=18 , then the maximum value of a^2,b^3,c^4 is equal to

If tangents P Q and P R are drawn from a point on the circle x^2+y^2=25 to the ellipse (x^2)/16+(y^2)/(b^2)=1,(b (a) (sqrt(5))/4 (b) (sqrt(7))/4 (c) (sqrt(7))/2 (d) (sqrt(5))/3

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