Question

If a+b+c= 16 and a²+b²+c²=200, Find the value of ab+bc+ca

Answer 1

Answer:

ab+bc+ca=28

Step-by-step explanation:

(a+b+c)²=a²+b²+c²+2(ab+bc+ca)

⇒16²=200+2(ab+bc+ca)

⇒256-200=2(ab+bc+ca)

⇒ab+bc+ca=56÷2

⇒ab+bc+ca=28

Answer 2

Step-by-step explanation:

$a + b + c = 16$

${a}^{2} + {b}^{2} + {c}^{2} = 200$

We know that,

(a + b + c)² = a² + b² + c² + 2(ab + bc + ac)

16² = 200 + 2(ab + bc + ac)

256 = 200 + 2(ab + bc + ac)

56 = 2(ab + bc + ac)

(ab + bc + ac) = 56/2

ab + bc + ac = 28