if 5-√6/5+√6=a-b√6,find the value of a and b
Answers
If 2+root3/2-root3=a+broot3,then find the value of 'a' and 'b'
https://brainly.in/question/6201068
this is ans
Step-by-step explanation:
Given:
\mathsf{\dfrac{5-\sqrt{6}}{5+\sqrt{6}}=a-b\sqrt{6}}
5+
6
5−
6
=a−b
6
\underline{\textbf{To find:}}
To find:
\textsf{The values of a and b}The values of a and b
\underline{\textbf{Solution:}}
Solution:
\mathsf{Consider,}Consider,
\mathsf{\dfrac{5-\sqrt{6}}{5+\sqrt{6}}=a-b\sqrt{6}}
5+
6
5−
6
=a−b
6
\mathsf{To\;rationalize\;the\;denominator\;of\;L.H.S}TorationalizethedenominatorofL.H.S
\mathsf{\dfrac{5-\sqrt{6}}{5+\sqrt{6}}{\times}\dfrac{5-\sqrt{6}}{5-\sqrt{6}}=a-b\sqrt{6}}
5+
6
5−
6
×
5−
6
5−
6
=a−b
6
\mathsf{\dfrac{(5-\sqrt{6})^2}{(5+\sqrt{6})(5-\sqrt{6})}=a-b\sqrt{6}}
(5+
6
)(5−
6
)
(5−
6
)
2
=a−b
6
\mathsf{\dfrac{(5-\sqrt{6})^2}{5^2-\sqrt{6}^2}=a-b\sqrt{6}}
5
2
−
6
2
(5−
6
)
2
=a−b
6
\mathsf{\dfrac{25+6-10\sqrt{6}}{25-6}=a-b\sqrt{6}}
25−6
25+6−10
6
=a−b
6
\mathsf{\dfrac{31-10\sqrt{6}}{19}=a-b\sqrt{6}}
19
31−10
6
=a−b
6
\mathsf{\dfrac{31}{19}-\dfrac{10}{19}\sqrt{6}=a-b\sqrt{6}}
19
31
−
19
10
6
=a−b
6
\textsf{Comparing on bothsides, we get}Comparing on bothsides, we get
\mathsf{a=\dfrac{31}{19}\;\;\&\;\;b=\dfrac{10}{19}}a=
19
31
&b=
19
10
\underline{\textbf{Find more:}}
Find more:
If 2+root3/2-root3=a+broot3,then find the value of 'a' and 'b'