Find a b values
5+√6/ = a+b√6
5-√6
full steps
Answers
Step-by-step explanation:
Answer:
\frac{5+\sqrt{6}}{5-\sqrt{6}}=\frac{31}{19}+\frac{+10\sqrt{6}}{19}
5−
6
5+
6
=
19
31
+
19
+10
6
Step-by-step explanation:
Given expression,
\frac{5+\sqrt{6}}{5-\sqrt{6}}
5−
6
5+
6
We have to rationalize the denominator of the given expression.
Consider,
\frac{5+\sqrt{6}}{5-\sqrt{6}}
5−
6
5+
6
Multiply and divide by 5 + √6
we get,
\implies\frac{5+\sqrt{6}}{5-\sqrt{6}}\times\frac{5+\sqrt{6}}{5+\sqrt{6}}⟹
5−
6
5+
6
×
5+
6
5+
6
\implies\frac{(5+\sqrt{6})^2}{(5-\sqrt{6})(5+\sqrt{6})}⟹
(5−
6
)(5+
6
)
(5+
6
)
2
\implies\frac{5^2+(\sqrt{6})^2+2\times5\times\sqrt{6}}{(5)^2-(\sqrt{6})^2}⟹
(5)
2
−(
6
)
2
5
2
+(
6
)
2
+2×5×
6
\implies\frac{25+6+10\sqrt{6}}{25-6}⟹
25−6
25+6+10
6
\implies\frac{31+10\sqrt{6}}{19}⟹
19
31+10
6
\implies\frac{31}{19}+\frac{+10\sqrt{6}}{19}⟹
19
31
+
19
+10
6
Therefore, \frac{5+\sqrt{6}}{5-\sqrt{6}}=\frac{31}{19}+\frac{+10\sqrt{6}}{19}
5−
6
this is ur answer
5+
6
=
19
31
+
19
+10
6