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Please forgive my unimagianative question, but is x2=2ypossible if both x and y are rational numbers?

Guest Apr 14, 2017
 #1
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Not possible......to see why let x =  a/b  and let y  = c/d   where a,b,c,d   are integers

 

Then we have that

 

(a/b)^2   =  2(c/d)^2   rearrange as

 

(a/b)^2 /(c/d)^2   = 2

 

(a^2 *d^2)  /  (b^2 *c^2)   = 2         take the square root of both sides

 

(a * d) / (b * c)  =  √2

 

But  a*d  , b*c     are both integers.......let a*d  = m  and b*c  = n

 

m / n  = √2

 

But......the square root of two is irrational....so.....we're led to a false conclusion.....thus, x and y  are not both rational

 

 

 

 

cool cool cool

CPhill  Apr 15, 2017

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