Solve the following simultaneous equations for `x` and `y`: `m(x+y)+n(x-y)-(m^(2)+mn+n^(2))=0, n(x+y)+m(x-y)-(m^(2)-mn+n^(2))=0`

Solve for x and y : mx- ny = m^(2) + n^(2) " " x - y = 2n

Solve the following system of equations by method of cross-multiplication: m x-n y=m^2+n^2,\ \ \ \ x+y=2m

If x^(m)y^(n)=(x+y)^(m+n)

The HCF of (x^(3)y)/(m^(2)n^(4)), (x^(2)y^(3))/(m^(2)n^(2)) and (x^(4)y^(2))/(mn^(3)) is

If m=sum_(r=0)^oo a^r n = sum_(r=0)^oo b^r, where 0,alt1, 0,blt1 then the quandratic equation whose roots are a and b is (A) mnx^2+(m+n-2mn)x=mn-m-n+1=0 (B) mnx^2+(2mn-m-n)x=mn-m-n+1=0 (C) mnx^2+(2mn+m+n)x=mn+m+n+1=0 (D) mnx^2+(2mn+m+n)x=mn+m+n+1=0

The area of the quadrilateral formed by two pairs of lines l^(2) x^(2)-m^(2) y^(2)-n(l x+m y)=0 and l^(2) x^(2)-m^(2) y^(2)-n(L x-m y)=0 is

If x^(m)y^(n)=(x+y)^(m+n) , then (dy)/(dx)=

If m =! n and (m + n)^(-1) (m^(-1) + n^(-1)) = m^(x) n^(y) , show that : x + y + 2 = 0.