Question

if a^2 + b^ 2 + c ^2= 20 and a+ b+ c = 0 find an+bc+ca​

Answer 1

$\huge\mathfrak\red{Answer:}$

Given:

• We have been given that  a² + b² + c² = 20 and a + b + c = 0.

To Find:

• We need to find the value of ab + bc + ca.

Solution:

As it is already given that  a² + b² + c² = 20 and a + b + c = 0, we can calculate the value of ab + bc + ca by this formula:

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

Substituting the given values, we have

(0)² = 20 + 2(ab + bc + ca)

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

=> (-20) = 2(ab + bc + ca)

=> -20/2 = ab + bc + ca

=> (-10) = ab + bc + ca

Verification:

a² + b² + c² + 2(ab + bc + ca)

=> 20 + 2(-10)

= 20 - 20

= 0

Hence verified!!

Therefore, the value of (ab + bc + ca) is -10.