Question

If 2^2008 – 2^2007 - 2^2006 + 2^2005 = k * 2^2005 then the value of k is equal to​

Answer 1

Explanation:

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if 2

2008

−2

2007

−2

2006

+2

2005

=k ⋅2

2005

then the value of k is equal to

Answer

Correct option is

B

3

2

2008

−2

2007

−2

2006

+2

2005

=k⋅2

2005

⇒[2

2008

−2

2006

]−[2

2007

−2

2005

]=k⋅2

2005

⇒2

2006

(2

2

−1)−2

2005

(2

2

−1)=k⋅2

2005

⇒3(2

2006

−2

2005

)=k⋅2

2005

⇒3[2

2005

(2−1)]=k⋅2

2005

⇒3(2

2005

)=k⋅2

2005

On comparing, we get

k=3

Hence, Option B is correct.

Answer 2

k = 3

Explanation:

`2^(2008)-2^(2007)-2^(2006)+2^(2005)=k * 2^(2005)`

`=> (2^(2005) * 2^3) - (2^(2005) * 2^2) - (2^(2005) * 2^1) + 2^(2005) = k * 2^(2005)`

• Take
  `2^(2005)` common from all the terms in L.H.S.

`=> 2^(2005)(2^3 - 2^2 - 2^1 + 1) = k * 2^(2005)`

• Divide both the sides by
  `2^(2005)`.

`=> (2^(2005)(2^3 - 2^2 - 2^1 + 1))/(2^(2005)) = (k * 2^(2005))/(2^(2005))`

`=> 2^3 - 2^2 - 2^1 + 1 = k`

• Expand the terms in L.H.S.

`=> 8 - 4 - 2 + 1 = k`

`=> k = 3`