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Question
If `2a + 1/(2a)` = 6, what will be the value of `64a^6 + 1/(64a^6)`?
Options
46656
39202
42592
36752
MCQ
Solution
39202
Explanation:
`2a + 1/(2a)` = 6
On squaring both side,
⇒ `(2a + 1/(2a))^2 = (6)^2`
⇒ `4a^2 + 1/(4a^2) + 2.2a. 1/(2a)` = 36
⇒ `4a^2 + 1/(4a^2)` = 34
Again, on cubing both side we get,
⇒ `64a^6 + 1/(64a^6) + 3.4a^2 . 1/(4a^2) (4a^2 + 1/(4a^2)) = (34)^3`
⇒ `64a^6 + 1/(64a^6) + 3 xx 34 = (34)^3`
⇒ `64a^6 + 1/(64a^6) = 34^3 - 3 xx 34`
= `34{(34)^2 - 3}`
= 34 × 1153
= 39202
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Algebraic Identities and Polynomials (Entrance Exam)
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