Question

show that irrational +,- irrational = rational​

Answer 1

Hey mate here is your answer

First, let us assume that an irrational number plus a rational number makes a rational number and make this lead to a contradiction.

If a is rational, b is irrational, and c is rational, we will try to prove that:

a + b = c

is rational. If this is true, a = x/y and c = e/f for integers x, y, e, and f. So:

a + b = c

==> x/y + b = e/f

==> b = e/f - x/y

==> b = ey/(fy) - xf/(fy)

==> b = (ey - xf)/(fy)

Since the RHS is rational, so is b. But we said that b is irrational! This leads to a contradiction and so the sum must be irrational.

I hope this helps!

karthikrikky12 ♥️