Question

if a square + b square + c square equals to 20 and a + b + c is equals to zero so a + b + BC + AC will be​

Answer 1

Correct Question

If a² + b² + c² = 20 and a + b + c = 0 then find the value of ab + bc + ac

Solution

Given

⇒a² + b² + c² = 20

⇒a + b + c = 0

To find

⇒Value of  ab + bc + ac

We know that

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

Now Put the value on this identities

⇒(0)² = 20 + 2(ab + bc + ac)

⇒0 = 20 + 2(ab + bc + ac)

⇒2(ab + bc + ac) = -20

⇒ab + bc + ac = -20/2

⇒ab + bc + ac = -10

Answer  

⇒ab + bc + ac = -10

Answer 2

Given :-

$\sf a^2+b^2+c^2=20$

$\sf a+b+c=0$

To Find :-

ab + bc + ca

Solution :-

By using the identity

$\sf (a+b+c)^2 = a^2+b^2+c^2+2(ab)+2(bc)+2(ac)$

Here,

$\sf (0)^2 = 20 + 2ab + 2bc + 2ac$

$\sf 0 = 20 + 2ab+2bc+2ac$

$\sf 0 = 20 + 2(ab + bc + ac)$

$\sf 0-20 = 2(ab+bc+ac)$

$\sf -20=2(ab+bc+ac)$

$\sf\dfrac{-20}{2} = ab + bc+ac$

$\sf -10 = ab+bc+ac$