Question

Show that any integer is of the form 6x,6x+1,6x+2,6x+3,6x+4,6x-1 for some integers x
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Consider the given equation,

6x

3

−11x

2

+6x−1=0

Put,x=1 we get

6.1

3

−11.1

2

+6.1−1=0

0=0

Hence, x=1 ⇒x−1=0 is zeroes os given equation.

Now

x−1

)6x

3

−11x

2

+6x−1

6x

2

−5x+1

−(6x

3

−6x

2

)

−5x

2

+6x−1

−(−5x

2

+5x)

x−1

−(x−1)

0

Now,

6x

2

−5x+1=0

6x

2

−3x−2x+1=0

3x(2x−1)−(2x−1)=0

(2x−1)(3x−1)=0

So,

6x

3

−11x

2

+6x−1=(2x−1)(3x−1)(x−1)=0

Hence, x=1,

2

1

,

3

1

in H.P.

Hence, this is the answer.