express with rational denominator 3+4√2 / 4+3√2
Answers
Step-by-step explanation:
We Know that
(a+b)(a−b)=a
2
−b
2
.....(1)
a
3
−b
3
=(a−b)(a
2
+ab+b
2
) .....(2)
Here in the problem the denominator has one power
2
1
and one power
3
1
. First we rationalize power
2
1
term ie.
2
and then rationalize power
3
1
term.
For doing so we multiply both numerator and denominator with
3
3
−
2
=
(
3
3
)
2
−2
(
2
3
3
)(
3
3
−
2
)
=
(
3
3
)
2
−2
(
3
3
)
2
2
−2
3
3
Let
3
3
=a,
2
=b
=
a
2
−b
2
a
2
b−b
2
a
Now multiplying both numerator and denominator with (a
4
+a
2
b
2
+b
4
)
=
(a
2
−b
2
)(a
4
+a
2
b
2
+b
4
)
(a
2
b−b
2
a)(a
4
+a
2
b
2
+b
4
)
=
a
6
−b
6
(ab)(a
5
+a
3
b
2
+ab
4
−a
4
b−a
2
b
3
−b
5
)
Substituting a,b in the above, we get
=
1
(
3
3
2
)[3(
3
3
)
2
+6+4
3
3
−3
3
3
2
−2(
3
3
)
2
2
−4
2
]
=3
2
.2
2
1
−3
3
5
.2+3
3
4
.2
2
3
−3.2
2
+3
3
2
.2
2
5
−3
3
1
.2
3
Answer:
Here's the attachment of the solution for your question.
Hope it helps
