Question

if a+b+c=0 and a square+b square +c square = 16 find the value of ac+bc+ca

Answer 1

Answer:

-8 is the value of (ab + bc + ca)

Step-by-step explanation:

Explanation:

Given, a + b + c = 0  and $a^2+ b^2 +c^2$ = 16 .

According to the question we need to find the value of (ac + bc + ca).

Now, as we know that the formula,

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

Step 1:

$(a + b + c)^2 = a^2 + b^2 +c^2 + 2ab + 2bc + 2ca$ can be written as

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

On putting the given values in the above formula we get,

0 = 16 + 2 (ab +bc + ca)

⇒2(ab + bc + ca) = - 16

⇒ab + bc + ca = $\frac{-16}{2}$ = -8

Final answer:

Hence, the value of ( ab + bc + ca ) is -8.

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Answer 2

Answer:

ab+bc+ac = -8

Step-by-step explanation:

Given,

a+b+c = 0

a²+b²+c² = 16

To find

ac+bc+ac

Recall the formula

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

Solution:

Since a²+b²+c² = 16 and a+b+c = 0

Substitute the above values in equation (A) we get,

0 = 16 + 2ab+2bc+2ac

2ab+2bc+2ac = -16

2(ab+bc+ac) = -16

ab+bc+ac = -8

∴ ab+bc+ac = -8

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