if p=2+1/p, find value of p^4-1/p^4
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Answer:
=322
Step-by-step explanation:
Consider p−
p
1
=4, squaring both sides, we get:
(p−
p
1
)
2
=4
2
⇒p
2
+(
p
1
)
2
−(2×p×
p
1
)=16(∵(a−b)
2
=a
2
+b
2
−2ab)
⇒p
2
+
p
2
1
−2=16
⇒p
2
+
p
2
1
=16+2
⇒p
2
+
p
2
1
=18
(p
2
+
p
2
1
)
2
=18
2
⇒(p
2
)
2
+(
p
2
1
)
2
+(2×p
2
×
p
2
1
)=324(∵(a+b)
2
=a
2
+b
2
+2ab)
⇒p
4
+
p
4
1
+2=324
⇒p
4
+
p
4
1
=324−2
⇒p
4
+
p
4
1
=322
Hence,
4
+
p
4
1
=322.
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