(5/(6-√3))+(3/(5+√3))
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Answered by
0
Answer:
3
5
−2
6
2
6
−
5
=
21
4
30
+9
Step-by-step explanation:
Given\: \frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}Given
3
5
−2
6
2
6
−
5
=\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}\times \frac{3\sqrt{5}+2\sqrt{6}}{3\sqrt{5}+2\sqrt{6}}=
3
5
−2
6
2
6
−
5
×
3
5
+2
6
3
5
+2
6
=\frac{2\sqrt{6}(3\sqrt{5}+2\sqrt{6})-\sqrt{5}(3\sqrt{5}+2\sqrt{6})}{(3\sqrt{5})^{2}-(2\sqrt{6})^{2}}=
(3
5
)
2
−(2
6
)
2
2
6
(3
5
+2
6
)−
5
(3
5
+2
6
)
=\frac{6\sqrt{30}+24-15-2\sqrt{30}}{45-24}=
45−24
6
30
+24−15−2
30
=\frac{4\sqrt{30}+9}{21}=
21
4
30
+9
Therefore,
\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}=\frac{4\sqrt{30}+9}{21}
3
5
−2
6
2
6
−
5
=
21
4
30
+9
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