If x−x
−1
=6, then the value of x
4
+x
−4
is:
- A1158
- B1154
- C1440
- D1442
Solution & Step-by-step Explanation
Given:
x−
x
1
=6
Squaring both sides:
(x−
x
1
)
2
=6
2
x
2
+
x
2
1
−2=36
x
2
+
x
2
1
=38
Squaring both sides again:
(x
2
+
x
2
1
)
2
=38
2
x
4
+
x
4
1
+2=1444
x
4
+
x
4
1
=1444−2=1442
x−
x
1
=6
Squaring both sides:
(x−
x
1
)
2
=6
2
x
2
+
x
2
1
−2=36
x
2
+
x
2
1
=38
Squaring both sides again:
(x
2
+
x
2
1
)
2
=38
2
x
4
+
x
4
1
+2=1444
x
4
+
x
4
1
=1444−2=1442