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If x=cy+bz, y=az+cx, and z=bx+ay, show that x2/1-a2=y2/1-b2=z2/1-c2

If x=cy+bz, y=az+cx, and z=bx+ay, show that x2/1-a2=y2/1-b2=z2/1-c2

Grade:

2 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
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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