Answer the following question
Answers
Answer:
a=
6
12
=2,b=
6
5
Step-by-step explanation:
Given :
\frac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}-2\sqrt{3}} = a - b\sqrt{6}
3
2
−2
3
2
+
3
=a−b
6
To Find :
The values of a & b,
Solution :
\frac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}-2\sqrt{3}}
3
2
−2
3
2
+
3
⇒ \frac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}-2\sqrt{3}} \times \frac{3\sqrt{2}+2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}
3
2
−2
3
2
+
3
×
3
2
+2
3
3
2
+2
3
⇒ \frac{(\sqrt{2}+\sqrt{3})(3\sqrt{2}+2\sqrt{3})}{(3\sqrt{2}-2\sqrt{3})(3\sqrt{2}+2\sqrt{3})}
(3
2
−2
3
)(3
2
+2
3
)
(
2
+
3
)(3
2
+2
3
)
⇒ \frac{6+ 2\sqrt{6} + 3\sqrt{6} + 6}{(3\sqrt{2})^2 - (2\sqrt{3})^2}
(3
2
)
2
−(2
3
)
2
6+2
6
+3
6
+6
⇒ \frac{12+ 5\sqrt{6}}{ 18 - 12}
18−12
12+5
6
⇒ \frac{12+ 5\sqrt{6}}{6}
6
12+5
6
⇒ a = \frac{12}{6}, b\sqrt{6} = \frac{5\sqrt{6}}{6}a=
6
12
,b
6
=
6
5
6
⇒ a = 2 , b = \frac{5}{6}a=2,b=
6
5