If `z=x+iy` and `|2z+1|=|z-3|`,then show that `3x^2+3y^2+10x=8`.

If a = x+y , b = y+z , and c = z+x then show that a^3+b^3+c^3-3abc =2(x^3+y^3+z^3-3xyz)

If x = 10 , y = 64, and z = 2, then prove that (x+y+z)^3 = 438976

If x = 32, y = -25 , and z = -7 , Then prove that x^3+y^3+z^3=16800

If x+y+z=6 , and xy+yz+zx=12 , then prove that x^3+y^3+z^3=3xyz

If z1=x1+iy1 and z2=x2+iy2 be two complex number,then show that bar(z1,z2)=bar z1.bar z2 .

If x = 658, y = 668, z = 674 , then prove that x^3+y^3+z^3-3xyz=392000

If x + y + z =xyz,show that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2).(2y)/(1-y^2).(2z)/(1-z^2)

If x = b + c - 2a, y = c + a-2b , z = a + b-2c , then prove that x^3+y^3+z^3-3xyz=0

If x = a^2 - b^2, y = 2ab, z = a^2+b^2 , then prove that x^6+y^6-z^6+3x^2y^2z^2=0

If x,y,z are in G.P then show that log_a x+log_a z=2/(log_y a),(x>0,y>0,z>0) .