If X=√3+√2/√3-√2, find (i) x^2+1/x^2 (ii) x^4+1/x^4
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Answer:
x+
x
1
=3−2
2
+
3−2
2
1
x
1
=
3−2
2
1
×
3+2
2
3+2
2
=
1
3+2
2
x+
x
1
=3−2
2
+3+2
2
=6
Squaring on 60th sides.
(x+
x
1
)
2
=36
x
2
+
x
2
1
=36−2⇒x
2
+
x
2
1
=34
Squaring on 60th sides.
(x
2
+
x
2
1
)
2
=(34)
2
x
4
+
x
4
1
=1156−2⇒x
4
+
x
4
1
=1154.
Step-by-step explanation:
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