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if x=cy+bz,y=az+cx,and z=bx+ay,show that x 2 /1-a 2 =y 2 /1-b 2 =z 2 /1-c 2

if x=cy+bz,y=az+cx,and z=bx+ay,show that 


x2/1-a2=y2/1-b2=z2/1-c2

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
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

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