Question

Arătați ca nr. a=(3 radical 2 - radical 3)² -(3 radical 2- radical 3)(3 radical 2 + radical 3) + 6 radical 6
este natural.​

Answer 1

Explicație pas cu pas:

a=(3√2-√3)²-(3√2-√3)(3√2+√3)+6√6

(3√2-√3)²=(3√2)²-2·3√2·√3+(√3)²

              =18-6√6+3

(3√2-√3)(3√2+√3)=(3√2)²-(√3)²

                            =18-3=15

a=18-6√6+3-15+6√6

a=6    6∈N⇒a∈N

Answer 2

a=(3√2-√3)²-(3√2-√3)(3√2+√3)+6√6

a=(3√2)²-2×3√2×√3+(√3)²-[(3√2)²-(√3)²]+6√6

a=18-6√6+3-(18-3)+6√6

a=18-6√6+3-15+6√6

a=6∈N