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

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

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

For a^(2)+b^(2)+c^(2)=1 and a,b,c are positive, the greatest value of a^(2)b^(3)c^(4) is 2^(x)3^(y) .Then the value of x is

If x=-1+sqrt(2), then the value of x^(3)+x^(2)-3x+6 is dots

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)

Prove that tan^2x+6lns e c x+2cosx+4>6secx for x\ in ((3pi)/2,\ 2pi)dot

If 2x+y=5 and 3x-4y=2, then the value of 2xy is (a) 4 (b) 6 (c) 8 (d) 10

The greatest integral value of a such that sqrt(9-a^(2)+2x-x^(2))>=sqrt(16-x^(2)) for at least one positive value of x is (a) 3 (b) 4 (c) 6 (d) 7

Prove that the value of each the following determinants is zero: (a^(x)+a^(-x))^(2),(a^(x)-a^(-x))^(2),1(b^(y)+b^(-y))^(2),(b^(y)-+b^(-y))^(2),1(c^(z)+c^(-z))^(2),(c^(z)-c^(-z))^(2),1]|