What will it give us when we subtract root 1 from root 5
Answers
Answer:
Hey friend,
Here is answer you were looking for:
\begin{gathered} \frac{ (\sqrt{5)} - 1 }{ (\sqrt{5}) + 1 } + \frac{( \sqrt{5}) + 1 }{( \sqrt{5}) - 1 } \\ \\ = \frac{( \sqrt{5} ) - 1}{( \sqrt{5}) + 1 } \times \frac{( \sqrt{5}) - 1 }{( \sqrt{5} ) - 1} + \\ \frac{( \sqrt{5} ) + 1}{( \sqrt{5} ) - 1} \times \frac{( \sqrt{5}) + 1 }{( \sqrt{5} ) + 1} \\ \\ = \frac{( \sqrt{5})^{2} + (1)^{2} + 2 \times ( \sqrt{5 )} \times 1 }{( \sqrt{5} )^{2} - (1)^{2} } \\ + \frac{( \sqrt{5})^{2} + {(1)}^{2} + 2 \times ( \sqrt{5}) \times 1 }{( \sqrt{5})^{2} - (1)^{2} } \\ \\ = \frac{5 + 1 - 2 \sqrt{5} }{5 - 1} + \frac{5 + 1 + 2 \sqrt{5} }{5 - 1} \\ \\ = \frac{6 - 2 \sqrt{5} + 6 + 2 \sqrt{5} }{4} \\ \\ = \frac{6 + 6}{4} \\ \\ = \frac{12}{4} \\ \\ = 3\end{gathered}
(
5
)+1
(
5)
−1
+
(
5
)−1
(
5
)+1
=
(
5
)+1
(
5
)−1
×
(
5
)−1
(
5
)−1
+
(
5
)−1
(
5
)+1
×
(
5
)+1
(
5
)+1
=
(
5
)
2
−(1)
2
(
5
)
2
+(1)
2
+2×(
5)
×1
+
(
5
)
2
−(1)
2
(
5
)
2
+(1)
2
+2×(
5
)×1
=
5−1
5+1−2
5
+
5−1
5+1+2
5
=
4
6−2
5
+6+2
5
=
4
6+6
=
4
12
=3