(1). 22
----------------- is equal to .......
2 + 3 + √5
(1) 3√3+ √5 - 2/15 - 4
(2) 3√3+√15
(3) 3√3+ √5 - 2/15 + 4
(4) 3√3+√5
.............................................................................
5-√3
(2).If x + y √3= ----------
2+√3
then the values of x and y respectively are........
(1) 13 and -7
(2) -13 and 7
(3) -13 and -7
(4) 13 and 7
.............................................................................
(3).If 3-2√5
----------- =a+b√5
6-√5
where a and b are rational numbers, then the values of a and b respectively are
(1)..8 -9
-----,,,,,, -----
35 35
(2)-8 9
---,,,,,,----
31 31
(3)-8 9
----,,,,,,----
35 35
(4)8 -9
----,,,,,,,----
31 31
.............................................................................
(4) If x = 1
--------
2-√3
then the value of (x - 1/x) is
(1) 4
(2) 2√3
(3) 2
(4)√3
.............................................................................
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Answers
Answer:
ANSWER
(i)
2
1
Let us assume
2
1
is rational.
So we can write this number as
2
1
=
b
a
---- (1)
Here, a and b are two co-prime numbers and b is not equal to zero.
Simplify the equation (1) multiply by
2
both sides, we get
1=
b
a
2
Now, divide by b, we get
b=a
2
or
a
b
=
2
Here, a and b are integers so,
a
b
is a rational number,
so
2
should be a rational number.
But
2
is a irrational number, so it is contradictory.
Therefore,
2
1
is irrational number.
(ii) 7
5
Let us assume 7
5
is rational.
So, we can write this number as
7
5
=
b
a
---- (1)
Here, a and b are two co-prime numbers and b is not equal to zero.
Simplify the equation (1) divide by 7 both sides, we get
5
=
7b
a
Here, a and b are integers, so
7b
a
is a rational
number, so
5
should be a rational number.
But
5
is a irrational number, so it is contradictory.
Therefore, 7
5
is irrational number.
(iii) 6+
2
Let us assume 6+
2
is rational.
So we can write this number as
6+
2
=
b
a
---- (1)
Here, a and b are two co-prime number and b is not equal to zero.
Simplify the equation (1) subtract 6 on both sides, we get
2
=
b
a
−6
2
=
b
a−6b
Here, a and b are integers so,
b
a−6b
is a rational
number, so
2
should be a rational number.
But
2
is a irrational number, so it is contradictory.
Therefore, 6+
2
is irrational number.