simplify 3/5-√3+2/5+√3
Answers
(5−
3
)
3
+
(5+
3
)
2
=
22
25+
3
Given:
\frac{3}{(5 - \sqrt{3})} + \frac{2}{(5 + \sqrt{3})}
(5−
3
)
3
+
(5+
3
)
2
Solution:
\frac{3}{(5 - \sqrt{3})} + \frac{2}{(5 + \sqrt{3})} = \left(\frac{3}{5 - \sqrt{3}} \times \frac{5 + \sqrt{3}}{5 + \sqrt{3}}\right) + \left(\frac{2}{5 + \sqrt{3}} \times \frac{5 - \sqrt{3}}{5 - \sqrt{3}}\right)
(5−
3
)
3
+
(5+
3
)
2
=(
5−
3
3
×
5+
3
5+
3
)+(
5+
3
2
×
5−
3
5−
3
)
=\frac{15 + 3 \sqrt{3}}{25 - 3} + \frac{10 - 2 \sqrt{3}}{25 - 3}=
25−3
15+3
3
+
25−3
10−2
3
=\frac{(15 + 3 \sqrt{3} + 10 - 2 \sqrt{3})}{22}=
22
(15+3
3
+10−2
3
)
\Rightarrow \frac{3}{(5 - \sqrt{3})} + \frac{2}{(5 + \sqrt{3})} = \frac{25 + \sqrt{3}}{22}⇒
(5−
3
)
3
+
(5+
3
)
2
=
22
25+
3
(5−
3
)
3
+
(5+
3
)
2
=
22
25+
3
Given:
\frac{3}{(5 - \sqrt{3})} + \frac{2}{(5 + \sqrt{3})}
(5−
3
)
3
+
(5+
3
)
2
Solution:
\frac{3}{(5 - \sqrt{3})} + \frac{2}{(5 + \sqrt{3})} = \left(\frac{3}{5 - \sqrt{3}} \times \frac{5 + \sqrt{3}}{5 + \sqrt{3}}\right) + \left(\frac{2}{5 + \sqrt{3}} \times \frac{5 - \sqrt{3}}{5 - \sqrt{3}}\right)
(5−
3
)
3
+
(5+
3
)
2
=(
5−
3
3
×
5+
3
5+
3
)+(
5+
3
2
×
5−
3
5−
3
)
=\frac{15 + 3 \sqrt{3}}{25 - 3} + \frac{10 - 2 \sqrt{3}}{25 - 3}=
25−3
15+3
3
+
25−3
10−2
3
=\frac{(15 + 3 \sqrt{3} + 10 - 2 \sqrt{3})}{22}=
22
(15+3
3
+10−2
3
)
\Rightarrow \frac{3}{(5 - \sqrt{3})} + \frac{2}{(5 + \sqrt{3})} = \frac{25 + \sqrt{3}}{22}⇒
(5−
3
)
3
+
(5+
3
)
2
=
22
25+
3