Please forgive my unimagianative question, but is x^{2}=2y^{2 }possible if both x and y are rational numbers?

Guest Apr 14, 2017

#1**+1 **

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

CPhill
Apr 15, 2017