Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
x
=
(
8
+
3
7
)
n
x = (8 + 3\sqrt{7})^n
x
=
(
8
+
3
7
)
n
, where
n
n
n
is a natural number, prove that the integral part of
x
x
x
is an odd integer and also show that
x
−
x
2
+
x
[
x
]
=
1
x - x^2 + x[x] = 1
x
−
x
2
+
x
[
x
]
=
1
, where
[
.
]
[. ]
[
.
]
denotes the greatest integer function.
Browse the problem library