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Question

If a2+1a2=34, then the value of a3+1a3 is equal to.

A
±234
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B
98
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C
±198
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D
±99
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Solution

The correct option is C ±198
It is given that
a2+1a2=34
Using identity we have
(a+1a)2=a2+1a2+2
(a+1a)2=34+2
(a+1a)2=36
(a+1a)2=62
(a+1a)=±6

Now, again from cubic identity we have,
a3+1a3=(a+1a)33(a)(1a)(a+1a)

Case I: When (a+1a) = +6,
a3+1a3=633(a)(1a)6
a3+1a3=63(3)(6)
a3+1a3=21618
a3+1a3=+198

Case II: When (a+1a) = -6,
a3+1a3=(6)33(a)(1a)(6)
a3+1a3=(6)3(3)(6)
a3+1a3=216+18
a3+1a3=198

Hence,
a3+1a3=±198

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