Question

x=6+3 radical din 2 si y = 6 -radical 18 aratati ca numerele x * y si x patrat + y patrat sunt numere intregi 

Answer 1

x * y = (6 + 3√2) * (6 - √18) = 36 - 6√18 + 18√2 - 3√36 = 36 - 18√2 + 18√2 - 3√36 = 36 - 3 * 6 = 36 - 18 = 18 ∈ Z

x² + y² = (6 + 3√2)² + (6 - √18)² = 36 + 36√2 + 18 + 36 - 12√18 + 18 = 108 ∈ Z

Answer 2

x=6+3√2
y=6-3√2
x*y=(6+3√2)(6-3√2)
=36-18=
=18∈ Z
x²+y²=(6+3√2)²+(6-3√2)²=
=36+36√2+18+36-36√2+18
=36+18+36+18
=108∈ Z