If x=2-√13/2 find the value of X2+1/x2
Answers
Answered by
3
Step-by-step explanation:
x=
2
3−
13
and
x
1
=
3−
13
2
.
We know, (x+
x
1
)
2
=x
2
+
x
2
1
+2
and x
2
+
x
2
1
=(x+
x
1
)
2
−2.
Now, x+
x
1
=
2
3−
13
+
3−
13
2
=
2(3−
13
)
(3−
13
)
2
+4
=
2(3−
13
)
9+13−6
13
+4
=
2(3−
13
)
26−6
13
=
2(3−
13
)
2
13
(
13
−3)
.
So x+
x
1
=−2
13
and (x+
x
1
)
2
=4×13=52.
x
2
+
x
2
1
=(x+
x
1
)
2
−2
=52−2=50.
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