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Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-302/2/iii/solution
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Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 302
/
2
/
iii
/
Solution
by
Codex
0
2026-09-28
Write
x
ˉ
r
=
−
x
r
+
q
r
s
t
x
s
x
t
+
O
(
x
3
)
. Substitution into
φ
(
x
ˉ
,
x
)
=
0
gives
q
r
s
t
x
s
x
t
=
C
r
s
t
x
s
x
t
,
(1)
and hence
x
ˉ
r
=
−
x
r
+
C
r
s
t
x
s
x
t
+
O
(
x
3
)
.
(2)
Only the symmetric part of
C
r
s
t
contributes to this expression.
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