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Standard XII
Mathematics
Evaluation of a Determinant
Show that the...
Question
Show that there is no positive integer n for which under root n-1 + under root n+1 is rational
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Similar questions
Q.
Show that there is no positive integer n for which
√
n
−
1
+
√
n
+
1
is rational.
Q.
The number of integers
′
n
′
such that the equation
n
x
2
+
(
n
+
1
)
x
+
(
n
+
2
)
=
0
has rational roots only, is
Q.
Consider the quadratic equation
n
x
2
+
7
√
n
x
+
n
=
0
, where
n
is a positive integer. Which of the following statements are necessarily correct?
I. For any
n
, the roots are distinct.
II. There are infinitely many values of
n
for which both roots are real.
III. The product of the roots is necessarily an integer.
Q.
What is the least integer
n
greater than
1
for which the square root of
n
, the cube root of
n
, and the fourth root of
n
are all integers?
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