- #1
rad0786
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Hi, can somebody please check my proof(s). I am pretty sure they are right...but i just feel they are too elelmentary.
1) Prove that 12 is irrational
-Let x be a rational number
-Therefore, x = {a/b: m in Z and n in N} n not 0.
-m and n have to be in the LOWEST FORMS...therefore, m and n cannot be divided any further and have no divisors
let x^2 =12
then (a/b)^2 = 12
then a^2/b^2=12
then (12)(b^2) = a^2
Contradiction since b^12 is divisiable by 12, hence b is divisable by 12
2. Prove that |x + y|^2 + |x - y|^2 = 2|x|^2 + 2|y|^2
|x + y|^2 + |x - y|^2
=(x+y)(x+y) + (x-y)(x-y)
=xx + 2xy + yy + xx -2xy + yy
=2xx +2yy
=2|x|^2 + 2|y|^2
Are the above correct?
1) Prove that 12 is irrational
-Let x be a rational number
-Therefore, x = {a/b: m in Z and n in N} n not 0.
-m and n have to be in the LOWEST FORMS...therefore, m and n cannot be divided any further and have no divisors
let x^2 =12
then (a/b)^2 = 12
then a^2/b^2=12
then (12)(b^2) = a^2
Contradiction since b^12 is divisiable by 12, hence b is divisable by 12
2. Prove that |x + y|^2 + |x - y|^2 = 2|x|^2 + 2|y|^2
|x + y|^2 + |x - y|^2
=(x+y)(x+y) + (x-y)(x-y)
=xx + 2xy + yy + xx -2xy + yy
=2xx +2yy
=2|x|^2 + 2|y|^2
Are the above correct?