if x=3+√5\2,show that x+1\x=3.
Answers
Answered by
1
We know that, (a+b)
3
=a
3
+b
3
+3ab(a+b)
x
3
+
x
3
1
=(2+
3
)
3
+
(2+
3
)
3
1
Here, taking (2+
3
)
3
⇒(2+
3
)
3
=2
3
+
3
3
+3×2×
3
(2+
3
)
=8+3
3
+6
3
(2+
3
)
=8+3
3
+12
3
+18
=26+15
3
Now, (2+
3
)
3
+
(2+
3
)
3
1
=26+15
3
+
26+15
3
1
Taking
26+15
3
1
⇒
26+15
3
1
×
26−15
3
26−15
3
=
676−675
26−15
3
=26−15
3
Now,
=26+15
3
+26−15
3
=52
Hence proved
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