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Mathematics
Mathematics
Problem
If the roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
ax^2 + bx + c = 0
a
x
2
+
b
x
+
c
=
0
are
k
+
1
k
\frac{k+1}{k}
k
k
+
1
and
k
+
2
k
+
1
\frac{k+2}{k+1}
k
+
1
k
+
2
, then prove that
(
a
a
+
b
+
c
)
2
=
k
2
(
k
+
1
)
2
\left( \frac{a}{a+b+c} \right)^2 = k^2 (k+1)^2
(
a
+
b
+
c
a
)
2
=
k
2
(
k
+
1
)
2
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