Question:
root 5 +root 2and2 root 5-3 root 3=a-b root 15 The find a+b
ans:
Answers
Step-by-step explanation:
Given :
\frac{ \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - 3 \sqrt{3} } = a - b \sqrt{15}
2
5
−3
3
5
+
3
=a−b
15
Let's simplify L.H.S by rationalising it's denominator.
\begin{gathered} \frac{ \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - 3 \sqrt{3} } \\ \\ \frac{ \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - 3 \sqrt{3} } \times \frac{2 \sqrt{5} + 3 \sqrt{3} }{2 \sqrt{5} + 3 \sqrt{3} } \\ \\ \frac{ \sqrt{5}(2 \sqrt{5} + 3 \sqrt{3} ) + \sqrt{3} (2 \sqrt{5} + 3 \sqrt{3} )}{(2 \sqrt{5}) {}^{2} - (3 \sqrt{3}) {}^{2} } \\ \\ \frac{10 + 3 \sqrt{15} + 2 \sqrt{15} + 9 }{20 - 27} \\ \\ \frac{19 + 5 \sqrt{15} }{ - 7} \end{gathered}
2
5
−3
3
5
+
3
2
5
−3
3
5
+
3
×
2
5
+3
3
2
5
+3
3
(2
5
)
2
−(3
3
)
2
5
(2
5
+3
3
)+
3
(2
5
+3
3
)
20−27
10+3
15
+2
15
+9
−7
19+5
15