If a+b=2 and a^2+b^2=6 show that ab=-1?

Question

Given that a+b = 2
and (a^2) + (b^2) = 6
Show that ab=-1
This is really simple, But I can't get it

Answer 1

a + b = 2 and a² + b² = 6

(a + b)² = a² + b² + 2ab

Substitute a + b = 2 and a² + b² = 6 then

2² = 6 + 2ab

4 = 6 + 2ab

Subtract 4 from each side

0 = 6 - 4 + 2ab

0 = 2 + 2ab

Subtract 2 from each side

-2 = -2 + 2 + 2ab

-2 = 0 + 2ab

-2 = 2ab

Recall : Symetric property a = b then b = a

2ab = -2

Divide each side by 2

ab = -1.