Can someone check this proof please?? NSG 2020 (1 Viewer)

[SadCeliac]

 

[SadCeliac]

I feel like I'm missing a key case or step here ^^

 

[yolo tengo]

View attachment 39412
View attachment 39413

i understood none of that

 

[mmmmmmmmaaaaaaa]

why wouldn’t you do:
assume a^2-4b=2 by contradictoon
a^2-4b-2=0
a^2=4b+2
=2(2b+1)
you know the rest

 

[synthesisFR]

this is horrible just drop

 

[SadCeliac]

why wouldn’t you do:
assume a^2-4b=2 by contradictoon
a^2-4b-2=0
a^2=4b+2
=2(2b+1)
you know the rest

am i stupid - let me redo this question

 

[SadCeliac]

this is horrible just drop

from me? yeah look, not my finest

 

[synthesisFR]

im just messing with u (all the time) dw about it lmfaoo

 

[SadCeliac]

why wouldn’t you do:
assume a^2-4b=2 by contradictoon
a^2-4b-2=0
a^2=4b+2
=2(2b+1)
you know the rest

@mmmmmmmmaaaaaaa could you please finish the solution I'm actually feeling super stupid rn

 

[synthesisFR]

i think like (from mmaaa)
assume a^2-4b=2 by contradictoon
a^2-4b-2=0
a^2=4b+2
a^2=2(2b+1)
my attempt dont laught:
lhs is integer
lhs is even
so a is even so
a=2m
so
4m^2=2(2b+1)
so
2b + 1= 2m^2
2b = 2m^2-1
dividing by 2 does not give b as integer?? bc m^2 is even so 2 m^2 is even so minus one is odd so not div by 2

 

[mmmmmmmmaaaaaaa]

@mmmmmmmmaaaaaaa could you please finish the solution I'm actually feeling super stupid rn

following on
a^2=4b+2
a^2=2(2b+1)
2a^2=2b+1
cant be even and odd at same time, contradictory

 

[SadCeliac]

So basically @mmmmmmmmaaaaaaa @synthesisFR this is it???

assume a^2 - 4b = 2
a^2 = 4b + 2
a^2 = 2(2b + 1) which is even
therefore a is even since a^2 is even
let a = 2m, m integral
therefore 4m^2 = 4b + 2
therefore 2m^2 = 2b + 1 which is odd

however because 2m^2 is even, and 2b + 1 is odd, there is a contradiction

therefore assumption is false

 

[mmmmmmmmaaaaaaa]

So basically @mmmmmmmmaaaaaaa @synthesisFR this is it???

assume a^2 - 4b = 2
a^2 = 4b + 2
a^2 = 2(2b + 1) which is even
therefore a is even since a^2 is even
let a = 2m, m integral
therefore 4m^2 = 4b + 2
therefore 2m^2 = 2b + 1 which is odd

however because 2m^2 is even, and 2b + 1 is odd, there is a contradiction

therefore assumption is false

yes

 

[SadCeliac]

 

[synthesisFR]

So basically @mmmmmmmmaaaaaaa @synthesisFR this is it???

assume a^2 - 4b = 2
a^2 = 4b + 2
a^2 = 2(2b + 1) which is even
therefore a is even since a^2 is even
let a = 2m, m integral
therefore 4m^2 = 4b + 2
therefore 2m^2 = 2b + 1 which is odd

however because 2m^2 is even, and 2b + 1 is odd, there is a contradiction

therefore assumption is false

yes u bufoon

 

[synthesisFR]

So basically @mmmmmmmmaaaaaaa @synthesisFR this is it???

assume a^2 - 4b = 2
a^2 = 4b + 2
a^2 = 2(2b + 1) which is even
therefore a is even since a^2 is even
let a = 2m, m integral
therefore 4m^2 = 4b + 2
therefore 2m^2 = 2b + 1 which is odd

however because 2m^2 is even, and 2b + 1 is odd, there is a contradiction

therefore assumption is false

thanks for literally copying my solutions brah

 

[SadCeliac]

you wouldn't need to use images if you latexed your math !!!!

I STILL DONT KNOW HOW TO AND I ACTUALLY TRIED WITH OVERLEAF

thanks for literally copying my solutions brah

I was just clarifying bae

 

[mmmmmmmmaaaaaaa]

thanks for literally copying my solutions brah

my solution you mean

 

[synthesisFR]

my solution you mean

I POSTED IT BEFORE U ASS BRO GET BACK TO STUDYING BC APPARANTLY THAT 96 EXT 2 MARK IS WEARING OFF

 

[synthesisFR]

omd u angry reacted to all of my messeges
i love u too