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If 2a+12a = 6, what will be the value of 64a6+164a6? -

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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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