The value of ( a+ 1/a) ( a-1/a) + {(a+1/a)} ^2 is
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Step-by-step explanation:
Simplifying the given expression,
(a+1)(a−1)(a
2
+1)=[(a+1)(a−1)]×(a
2
+1)
=(a
2
−1
2
)×(a
2
+1)[Using the identity (x+y)(x−y)=x
2
−y
2
]
=(a
2
−1)(a
2
+1)
=(a
2
)
2
−1[Using the identity (x+y)(x−y)=x
2
−y
2
]
=a
4
−1
Hence, the given statement is true.
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