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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?