Question

Cho a+b+c = 9 ; a²+b²+c²= 53 , tính ab+ac+bc

Answer 1

a + b +c = 9

( a+b+c )^2 = 9^2

a^2 + b^2 +c^2 + 2ab+ 2bc +2ac = 81

53 + 2(ab+bc+ac) = 81

         2(ab+bc+ac)  = 81 - 53

         2(ab +bc +ac) = 28

            ab + bc +ac  = 14

Answer 2

a² + b² + c² = 53 
Ta có

(a+b+c)²=a²+b²+c² + 2ab+2ac+2bc = 9² (1) 
thay a² + b² + c² = 53 vào (1)

=> 53 +2ab+2ac+2bc = 9² 

=>2ab+2ac+2bc = 9² - 53 
=> 2ab+2ac+2bc = 28 
=> 2.(ab+bc+ca)=28

=> ab+bc+ca = 28:2 = 14