Question

If a + b + c is equals to 4 and a square + b square + c square is equals to 14 find AB + BC + AC

Answer 1

Answer:

(ab+bc+ca)=1

Step-by-step explanation:

(a+b+c)^2 =a^2+b^2+c^2+2(ab+bc+ca)

16-14=2(ab+bc+ca)

2/2=(ab+bc+ca)

(ab+bc+ca)=1

Answer 2

AB + BC + AC=1

Given:

a + b + c= 4

a² + b² + c²= 14

To find:

AB + BC + AC

Solution:

As we know,

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

Now putting the value of (a² + b² + c),we have,

                  = 14 + 2(ab + bc + ca

         ⇒ 4² = 14 + 2(ab + bc + ca)    {As given in the question a + b + c = 4}

         ⇒ 16 = 14 + 2(ab + bc + ca)

         ⇒  2 = 2(ab + bc + ca)

         ⇒ 1   =  ab + bc + ca

According to the question we need to find AB + BC + AC.

So if we take,

AB = ab

BC = bc

AC = ca.

Then,

AB + BC + AC= 1 as we have solve in the above.

Therefore, AB + BC + AC = 1

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