Math, asked by hari5674, 8 months ago

for 10 class 2nd question​

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Answered by khushisemra0881
4

Here is your answer user.

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Answered by amitkumar44481
3

QuestioN :

Show that any positive odd integer is of the form 6q + 1 , or 6q + 3 , 6q + 5, Where q is some integer.

SolutioN :

We have, General Equation.

 \tt \dagger \:  \:  \:  \:  \: \fbox{ a = bq + r.}

Let the positive integer which is divisible by n.

 \tt \longmapsto n = 6q + r.

 \tt \dagger \:  \:  \:  \:  \:  r = 0,1,2,3,4,5. \:  \:  \:  \:  \: (r < 6)

Case 1.

When r = 0.

 \tt \longmapsto n = 6q + 0.

 \tt \longmapsto n = 6q

Even.

\rule{90}2

Case 2.

When, r = 1.

 \tt \longmapsto n = 6q + 1.

Odd.

\rule{90}2

Case 3.

When, r = 2.

 \tt \longmapsto n = 6q + 2.

Even.

\rule{90}2

Case 4.

When, r = 3.

 \tt \longmapsto n = 6q + 3.

Odd.

\rule{90}2

Case 5.

When, r = 4.

 \tt \longmapsto n = 6q + 4.

Even.

\rule{90}2

Case 6.

When, r = 5.

 \tt \longmapsto n = 6q + 5.

Odd.

Hence Proved.

6q + 1 , or 6q + 3 , 6q + 5 is odd positive integer.

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