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Mathematics
Mathematics
Problem
If
α
,
β
\alpha, \beta
α
,
β
are the roots of the equation
x
2
−
(
5
+
3
log
3
5
−
5
log
5
3
)
x
+
3
(
3
(
log
9
55
)
1
3
−
5
(
log
5
3
)
2
3
−
1
)
=
0
x^2 - \left(5 + 3\sqrt{\log_3 5} - 5\sqrt{\log_5 3}\right)x + 3\left(3^{(\log_9 55)^{\frac{1}{3}}} - 5^{(\log_5 3)^{\frac{2}{3}}} - 1\right) = 0
x
2
−
(
5
+
3
lo
g
3
5
−
5
lo
g
5
3
)
x
+
3
(
3
(
l
o
g
9
55
)
3
1
−
5
(
l
o
g
5
3
)
3
2
−
1
)
=
0
then the equation, whose roots are
α
+
1
β
\alpha + \frac{1}{\beta}
α
+
β
1
and
β
+
1
α
\beta + \frac{1}{\alpha}
β
+
α
1
(A)
3
x
2
−
20
x
−
12
=
0
3x^2 - 20x - 12 = 0
3
x
2
−
20
x
−
12
=
0
(B)
3
x
2
−
10
x
−
4
=
0
3x^2 - 10x - 4 = 0
3
x
2
−
10
x
−
4
=
0
(C)
3
x
2
−
10
x
+
2
=
0
3x^2 - 10x + 2 = 0
3
x
2
−
10
x
+
2
=
0
(D)
3
x
2
−
20
x
+
16
=
0
3x^2 - 20x + 16 = 0
3
x
2
−
20
x
+
16
=
0
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