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Mathematics
Problem
For the curve defined by
x
2
+
x
y
+
y
2
=
7
x^{2}+xy+y^{2}=7
x
2
+
x
y
+
y
2
=
7
, which of the following expressions equals
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
in terms of
x
x
x
and
y
y
y
? a)
42
(
x
+
2
y
)
3
\displaystyle \frac{42}{(x+2y)^{3}}
(
x
+
2
y
)
3
42
b)
−
42
(
2
x
+
y
)
3
\displaystyle -\frac{42}{(2x+y)^{3}}
−
(
2
x
+
y
)
3
42
c)
2
(
x
−
y
)
(
x
+
2
y
)
2
−
2
(
2
x
+
y
)
2
(
x
+
2
y
)
3
\displaystyle \frac{2(x-y)}{(x+2y)^{2}}-\frac{2(2x+y)^{2}}{(x+2y)^{3}}
(
x
+
2
y
)
2
2
(
x
−
y
)
−
(
x
+
2
y
)
3
2
(
2
x
+
y
)
2
d)
−
42
(
x
+
2
y
)
2
\displaystyle -\frac{42}{(x+2y)^{2}}
−
(
x
+
2
y
)
2
42
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