Question

if, x=cy+bz, y=az+cx, z=ax+by ; then proove that [x^2/(1-a^2) = y^2/(1-b^2) = z^2/(1-c^2)]

Answer 1

Hello student,

x = cy + bz

y = az + cx

y = az + c^2y + cb

(1 - c^2)y = (a+bc)z

meanwhile

z = bx + ay

z = bcy + b^2z + ay

(1 - b^2)z = (a + bc)y

from first set:

y/(a+bc) = z/(1 - c^2)

(a + bc)y/(1 - b^2) = z

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

y^2/(1 - b^2) = z^2/(1 - c^2)

then you can continue with the rest of the equation...

Hope it helps...