Question

Given, x=cy+bz, y=az+cx & z=bx+ay. Prove, x^2:y^2:z^2=(1-a^2):(1-b^2):(1-c^2).

Answer 1

x = cy + bz 

y = az + cx 

y = az + c²y + cb 

(1 - c²)y = (a+bc)z 

meanwhile 

z = bx + ay 

z = bcy + b²z + ay 

(1 - b²)z = (a + bc)y

 from first set:

 y/(a+bc) = z/(1 - c²) 

(a + bc)y/(1 - b²) = z 

multiply left equation to left.. and right equation to right equation also . 

y²/(1 - b²) = z²/(1 - c²) 

then you can continue with the rest of the equation