1 1 If x² +1/x²=11,find the value of i)x - 1/x ii)x⁴+ 1/x⁴
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Correct option is D)
Given x+
x
1
=5
let y=x
4
+
x
4
1
x+
x
1
=5
Squaring on both sides
(x+
x
1
)
2
=5
2
⇒x
2
+
x
2
1
+2(x)(
x
1
)=25
⇒x
2
+
x
2
1
+2=25
⇒x
2
+
x
2
1
=23
Squaring on both sides
⇒(x
2
+
x
2
1
)
2
=23
2
⇒x
4
+
x
4
1
)+2(x
2
)(
x
2
1
)=529
⇒x
4
+
x
4
1
+2=529
⇒x
4
+
x
4
1
=527
⇒y=527
Thus, required term value is 527.
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