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Mathematics
Problem
Given, x = cy + bz, y = az + cx and
z
=
b
x
+
a
y
\sqrt{z} = bx + ay
z
=
b
x
+
a
y
, where x, y and z are not all zero, prove that
a
2
+
b
2
+
c
2
+
2
a
b
c
=
1
a^2 + b^2 + c^2 + 2abc = 1
a
2
+
b
2
+
c
2
+
2
ab
c
=
1
.
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