Question

Find the integers m and n such that (m+n√2)(1-√2)²=-2+2√2​

Answer 1

m = n = 2

Explanation:

(m + n√2)(1 - √2)² = -2 + 2√2

(m + n√2)(1 - 2√2 + 2) = -2 + 2√2

(m + n√2)(3 - 2√2) = -2 + 2√2

3m - 2m√2 + 3n√2 - 4n = - 2 + 2√2

(3n - 2m)√2 + 3m - 4n = 2√2 - 2

3n - 2m = 2

4n - 3m = 2

3n - 2m = 4n - 3m

n = m

4n - 3n = 2

n = 2

m = 2