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Mathematics
Mathematics
Problem
Prove that
∣
1
+
a
1
1
1
1
+
b
1
1
1
1
+
c
∣
=
a
b
c
(
1
+
1
a
+
1
b
+
1
c
)
\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = abc \left( 1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)
1
+
a
1
1
1
1
+
b
1
1
1
1
+
c
=
ab
c
(
1
+
a
1
+
b
1
+
c
1
)
hence find the value of the determinant, if
a
,
b
a, b
a
,
b
and
c
c
c
are the roots of the equation
p
x
3
−
q
x
2
+
r
x
−
s
=
0
px^3 - qx^2 + rx - s = 0
p
x
3
−
q
x
2
+
r
x
−
s
=
0
.
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