Math, asked by dushyantsanwal, 1 year ago

show that any positive integer is of the form 3q or 3q + 1 or 3q + 2

Answers

Answered by Moumita07
6
Let x be the integer
x=3q
x²=9q²
x²=3(3q²)
x²=3q [let 3q² be q]

x=3q+1
x²=(3q+1)²
x²=9q²+6q+1
x²=3(3q²+2q)+1
x²=(3q+1) [let 3q²+2q be q]

x=3q+2
x²=(3q+2)²
x²=9q²+12q+4
x²=3(3q²+4q+1)+1
x²=(3q+1) [3q²+4q+1 be q]

it proves q² is in the form of 3q and (3q+1) but not in the form of (3q+2)
May this helful

himanshu222133patzks: In my school they showed the same method but I am no able to understand the logic behind this thing....can any one tell me
Moumita07: let check on youtube...u cn understand clearly
Moumita07: if u help thn mrk as braunliest
Moumita07: brai*n
Answered by fanbruhh
5
 \huge \bf{ \red{hey}}

 \huge{ \mathfrak{ \blue{here \: is \: answer}}}

let a be any positive integer

then

b= 3

a= bq+r

0≤r<b

0≤r<3

r= 0,1,2

case 1.

r=0

a= bq+r

3q+0

3q

case 2.

r=1

a= 3q+1

3q+1

case3.

r=2

a=3q+2

hence from above it is proved that any positive integer is of the form 3q,3q+1 and 3q+2

 \huge \boxed{ \boxed{ \green{HOPE\: IT \: HELPS}}}

 \huge{ \pink{thanks}}
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