Question

if a+b+c=4 a2+b2+c2=14 find the value of ab+bc+ca

Answer 1

a+b+c=4
a2+b2+2c=14
ab+bc+ac=8

Answer 2

The value of ab + bc + ca is 1.

Given:

The value of a + b + c = 4

The value of a² + b² + c² = 14.

To Find:

The value of ab + bc + ca =?

Solution:

To calculate the value of (ab + bc + ca), we will use the following formula:

i.e., (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Now, By substituting the values given above, we get;

⇒ (4)² = 14 + 2(ab + bc + ca)

⇒ 16 = 14 + 2(ab + bc + ca)

⇒  2(ab + bc + ca) = 16 - 14

⇒  2(ab + bc + ca) = 2

⇒  (ab + bc + ca) = 1

Thus, the value of ab + bc + ca is 1.

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