Math, asked by AbdulPatel, 1 year ago

if 'n' is an integer,then show that
 {n}^{2}
is divisible by 8


MitheshShankar: Show that n2-1 is divisible by 8, if n is an odd positive integer.
MitheshShankar: this is the question

Answers

Answered by Aditya1861
1
put the value of n 1
then we get 8*1 = 8

put the value of n 2
then we get 8*4= 32

put the value of n 3
then we get 8*9 = 72

So n2 is divisible by 8

Hope It will help you
please Mark me as brainlest

Aditya1861: why
Aditya1861: it is right
MitheshShankar: his question is wrong and in that question you modified it a little bit by multiplying 2 instead of squaring
Aditya1861: ok
Aditya1861: I changed the answer by squaring it
AbdulPatel: my question is not wrong..... this question is in maths sample paper from DEO.
MitheshShankar: the question is prove n^2 is divisible by 8?
MitheshShankar: is that a 1 mark question ?
AbdulPatel: this question is for 3 marks
MitheshShankar: what? impossible
Answered by MitheshShankar
1
for the question "Show that n2-1 is divisible by 8, if n is an odd positive integer."

here is the solution 

Any odd positive integer is of the form

4m + 1 or 4m + 3 for some integer m.

 When n = 4m + 1,

 n2 – 1 = (4m + 1)2 – 1

= 16
 m^{2}  +8m+1 – 1

= 16
m ^{2} +8m

= 8m(2m+1) 
 n^{2}  – 1 is divisible by 8. When n = 4m + 3 n ^{2} – 1

 = (4m+3) – 1 = 16
m ^{2} + 24m + 9 – 1

= 16
m ^{2} + 24m + 8 = 8(2m ^{2} + 3m + 1) n ^{2}  – 1 is divisible by 8.
 
Hence, 
n ^{2} – 1 is divisible by 8 if n is an odd positive integer.
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