Given x=cy+bz,y=az+cx and z=bx+ay, then prove `a^(2) +b^(2) +c^(2) `+2abc =1.

If f(x)= y = (ax-b)/(cx-a) , then prove that f(y) = x

If y =(ax +b)/( cx + d) , then prove that 2y_1y_3=3(y_2)^2

If ax+cy+bz=X, cx+by+az=Y, bx+ay+cz=Z, show that (a^(2)+b^(2)+c^(2)-bc-ca-ab)(x^(2)+y^(2)+z^(2)-yz-zx-xy)=X^(2)+Y^(2)+Z^(2)-YZ-ZX-XY

If y= e^(ax) sin bx then show that, y_(2)- 2ay_(1) + (a^(2) + b^(2))y= 0

If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

Prove the followings : If cos^(-1)a+cos^(-1)b+cos^(-1)c=pi then a^(2)+b^(2)+c^(2)+2abc=1 .

If x=1+(log)_a b c , y=1+(log)_b c a and z=1+(log)_c a b , then prove that x y z=x y+y z+z x

If x-iy = sqrt((a+ib)/(c-id)) , prove that (x^(2) + y^(2))^(2) = (a^(2) + b^(2))/(c^(2) + d^(2))

If y=xlog(x/(a+bx)) , then prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

If ax + by = a^(2)-b^(2) and bx + ay = 0, find the value of x + y .