[" If "(x+a)^(2)+(y+b)^(2)=4(ax+by)" ,where "x" ,"],[a,y,b" are real,the value of "xy-ab" is : "]

Let x,y,z are positive real numbers satisfying x+y+z=1 . If the maximum value of x^(3)y^(2)z can be expressed as (a)/(b) where a and b are co-prime,then the value of (a+b) is

If 2 - i is a root of the equation ax^2+ 12x + b=0 (where a and b are real), then the value of ab is equal to :

If xy=a^(2) and S=b^(2)x+c^(2)y where a,b and c are constants then the minimum value of S is

If 4x^(2) + 12xy -8x+9y^(2) -12y = (ax+by) (ax+by-4) , then the value of a^(2) +b^(2) is

If xy=a^2 and S = b^2x + c^2y where a, b and c are constants then the minimum value of S is

If 4x ^(2) + 12 xy - 8x + 9 y ^(2) - 12 y = (ax + by) (ax+ by -4), then the value of a ^(2) +b ^(2) is

If log_(10)(x^(3)+y^(3))-log_(10)(x^(2)+y^(2)-xy)<=2, where x,y are positive real number,then find the maximum value of xy.

If a=xy^(2) and b=x^(3)y^(5) where x and y are prime numbers then LCm of (a,b) is _____________.