If `2X=4Y=8Z`,then find `X:Y:Z`

If X = 5Y = 8Z, find X:Y:Z.

If [x y4z+6x+y]=[8w0 6] , then find the values of x ,\ y ,\ z\ a n d\ w .

If x+y -z = 4 and x^(2) + y^(2) + z^(2) = 30 , then find the value of xy- yz- zx

If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(z y-z)+cot^(-1)(z x+1)/(z-x)

If z_1=9y^2-4-10ix, z_2=8y^2-20i, where z_1=overline z_2, then find z=x+iy

If [(x,3x-y),(2x+z,3y-w)]=[(3,2),(4,7)], then find x+y+z+w.

If 2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(8z)=4 find the value of x.

If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}] , then find the values of x,y,z and w.

If x,y,z in R and |{:(x,y^2,z^3),(x^4,y^5,z^6),(x^7,y^8,z^9):}|=2 then find the value of |{:(y^5z^6(z^3-y^3),x^4z^6(x^3-z^3),x^4y^5(y^3-x^3)),(y^2z^3(y^6-z^6),xz^3(z^6-x^6), xy^2(x^6-y^6)),(y^2z^3(z^3-y^3),xz^3(x^3-z^3),xy^2(y^3-x^3)):}|

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1). x y+y z+z y and (2). x(y+z)+y(z+x)+z(x+y)