If `3^x=5^y=(75)^z` show that `z=(xy)/(2x+y`

If 2^(x)=3^(y)=12^(z) show that xy=z(x+2y)

if 3^(x)=5^(y)(75)^(z) then Z=

If x+y+z=0 show that x^3+y^3+z^3=3x y z .

If z=x+iy and |z+a|=3|z-a|, show that 2(x^2+y^2)=5ax-2a^2 .

If (x+y+z)(y+z-x)(z+x-y)(x+y-z) prop x^2y^2 then show that either x^2+y^2= z^2 or x^2+y^2-z^2 prop xy .

If x+y+z=xyz , prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/(1-3z^(2))= (3x-x^(3))/(1-3x^(2)).(3y-y^(3))/(1-3y^(2)).(3z-z^(3))/(1-3z^(2)) b) (x+y)/(1-xy) + (y+z)/(1-yz)+(z+x)/(1-zx)= (x+y)/(1-xy) .(y+z)/(1-yz).(z+x)/(1-zx)

By using properties of determinants , show that : {:|( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) |:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

By using properties of determinants , show that : {:[( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) ]:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

By using properties of determinants , show that : {:[( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) ]:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

Using properties of determinant show that : |((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3