Question

Ifa²+b²+c²=20,and a+b+c=0,find ab+bc+ca.

Answer 1

Answer:

Step-by-step explanation:

Given a2+b2+C2=20

a+b+c=0

Using identity-

(a+b+c)2= a2+b2+C2+2ab+2bc+2c (a+b+c)2 =a2+b2+C2+2(ab+bc+ca)

(0)2 =20+2(ab+bc+ca)

- 20 =2(ab+bc+ca)

-20÷2 =(ab+bc+ca)

-10 = (ab+bc+ca) ans

Hope it will help you.

Answer 2

Answer:

We have,

$\tt \qquad {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + { c}^{2} \\ \qquad \tt + 2ab + 2bc + 2ca \\ \\ \\ \implies \tt {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} \\ \tt + 2(ab + bc + ca) \\ \\ \\ \implies \tt {0}^{2} = 20 + 2 \: (ab + bc + ca) \\ \\ \\ \implies \sf \frac{ - 20}{2} = \bigg \{ \frac{2(ab + bc + ca)}{2} \bigg \} \\ \\ \\ \implies \tt \: - 10 = ab + bc + ca \\ \\ \\ \implies \boxed {\tt ab + bc + ca = - 10}$