" 8.If "3^(x)=5^(y)=(75)^(z)," show that "z=(xy)/(2x+y)

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

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

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

If (3x-5y)/5z+3y)=(x+5z)/(y-5x)=(y-z)/(x-z) then show that each ratio is x/y .

If x^(3)+y^(3)+z^(3)=3xyz and x+y+z=0, find the value of ((x+y)^(2))/(xy)=((y+z)^(2))/(yz) +((z+x)^(2))/(zx)

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

Using the properties of determinants, show that: abs((x,x^2,yz),(y,y^2,xz),(z,z^2,xy))=(x−y)(y−z)(z−x)(xy+yz+zx)

Show that |(x,x^(2),yz),(y,y^(2),zx),(z,z^(2),xy)|=(x-y)(y-z)(z-x)(xy+yz+zx)