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Mathematics
Mathematics
Problem
If
x
2
+
y
2
=
t
−
1
x^2 + y^2 = t^{-1}
x
2
+
y
2
=
t
−
1
and
x
4
+
y
4
=
t
2
+
1
t
2
x^4 + y^4 = t^2 + \frac{1}{t^2}
x
4
+
y
4
=
t
2
+
t
2
1
, then prove that
d
y
d
x
=
1
x
3
y
\frac{dy}{dx} = \frac{1}{x^3 y}
d
x
d
y
=
x
3
y
1
.
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