Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
a
>
0
a > 0
a
>
0
. If the function
f
(
x
)
=
6
x
3
−
45
a
x
2
+
108
a
2
x
+
1
f(x) = 6x^3 - 45ax^2 + 108a^2x + 1
f
(
x
)
=
6
x
3
−
45
a
x
2
+
108
a
2
x
+
1
attains its local maximum and minimum values at the points
x
1
x_1
x
1
and
x
2
x_2
x
2
respectively such that
x
1
x
2
=
54
x_1x_2 = 54
x
1
x
2
=
54
, then
a
+
x
1
+
x
2
a + x_1 + x_2
a
+
x
1
+
x
2
is equal to :-
Browse the problem library