# Irrational identity?

How do you deduce that

a1 - $\sqrt{N}$ b1 = a2 - $\sqrt{N}$b2

to be

a1=a2 and b1=b2?

Matching coefficients?

You can't: Take N = 4, a1=5, b1=1, a2=15, and b2=6

You can't: Take N = 4, a1=5, b1=1, a2=15, and b2=6

In this case, they are only equal because N is a perfect square.

If a + b√N = c + d√N, then
a - c = (d - b)√N

Assuming a, b, c, d are integers, then (a - c) is an integer, thus for equality, (d - b)√N must be an integer. This is only true if a = c and b = d, or if √N is an integer, making N a perfect square.

Last edited:
Hey guys,

I see now...Thanks! Appreciate it.

disregardthat