If (x ^ 2 - y ^ 2)/(x ^ 2 + y ^ 2) + (x ^ 2 + y ^ 2)/(x ^ 2 - y ^ 2) = sqrt(2) , then (x ^ 8 - y ^ 8)/(x ^ 8 + y ^ 8) =
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Answer:
Solution
x=
2
−1
2
+1
=(
2
−1
2
+1
)×
2
+1
2
+1
=
2−1
(
2
+1)
2
∴x=
3+2
2
y=
2
+1
2
−1
=
2
+1
2
−1
×
2
−1
2
−1
=
2−1
(
(2−1)
2
)
∴y=
3−2
2
∴xy=(3+2
2
)
2
+(3−2
2
)
∴
xy
=9−8=
1
Now x
2
+y
2
=(3+2
2
)
2
+(3−2
2
)
2
=9+8+12
2
+9+8−12
2
∴
x
2
+y
2
=34
∴x
2
+y
2
+xy=34+1=35
∴x
2
+y
2
+xy=35
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