if √6-5 /√6+5 = a+b√30 find a and b
Answers
Answer:
The values of a and b are 11 and
2 respectively. 2 respectively.
Given:
{sqrt6+sqrt5}{sqrt6-sqrt5}=a+bsqrt{30}
6
−
5
6
+
5
=a+b
30
To find:
{The value of a and b.}The value of a and b.
Solution:
{a+b sqrt{30}={sqrt6+sqrt5}{sqrt6-sqrt5}}a+b
30
=
6
−
5
6
+
5
{therefore{a+b sqrt{30}=dfrac{sqrt6+sqrt5)^{2}}{(sqrt6-sqrt5)(sqrt6+sqrt5)}}}∴a+b
30
=
(
6
−
5
)(
6
+
5
)
(
6
+
5
)
2
{therefore{a+b sqrt{30}={6+5+2 sqrt{30}}{6-5}}}∴a+b
30
=
6−5
6+5+2
30
{therefore{a+b sqrt{30}={11+2 sqrt{30}}{1}}}∴a+b
30
=
1
11+2
30
{therefore{a+b sqrt{30}=11+2sqrt{30}}}∴a+b
30
=11+2
30
On comparing we get On comparing we get,
a=11 and b sqrt{30}=2 sqrt{30}}a=11 and b
30
=2
30
therefore a=11 and b=2∴a=11 and b=2
The values of a and b are 11 and∴The values of a and b are 11 and 2 respectively.