if x + 1/x = √3 then x=
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x+
x
1
=
3
Cubing both the sides.
x
3
+
x
3
1
+3(x+
x
1
)=3
3
⇒x
3
+
x
3
1
+3(
3
)=3
3
x
3
+
x
3
1
=0⇒
x
3
x
6
+1
=0
x
6
+ 1 = 0
Now, x
18
+x
12
+x
6
+1
⇒x
12
(x
6
+1)+(x
6
+1)
From (1) x
12
(0) + (0) = 0
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