Find the maximum value of `x^m y^n, m, n > 0` such that `x + y = a.`

If y ^(2)(y^(2) -6) + x ^(2) -8x +24 =0 and the minimum value of x ^(2) + y^(4) is m and maximum value is M, then find the value of M-2m.

If y ^(2)(y^(2) -6) + x ^(2) -8x +24 =0 and the minimum value of x ^(2) + y^(4) is m and maximum value is M, then find the value of M-2m.

The value of log_(x^(n))y^(m) is

If x, y, k, m, n are positive and x + y = k, then find the maximum value of x^(m)y^(n) .

Find the value of m&n for which the system of Linear equation has infinity many solutions.3x+4y=12(m+n)x+2(m-n)y=5m-1

Let log x= 2m - 3n and log y = 3n - 2m Find the value of log (x^(3) /y ^(2)) in terms of m and n.

If (x-y)^(m+n)=x^m.y^n , show that dy/dx=y/x