Question

If a+b=0 and a square+b square+c square=16, find the value of ab+bc+ca.

Answer 1

Answer :

Given, a + b + c = 0 ...(i)
and a² + b² + c² = 16 ...(ii)

We know that,

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

⇒ 0² = 16 + 2(ab + bc + ca), by (i) and (ii)

⇒ 2(ab + bc + ca) = - 16

⇒ ab + bc + ca = - 16/2

⇒ ab + bc + ca = - 8

∴ ab + bc + ca = - 8

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Answer 2

hey friend!!!!

your answer is "-8"

Explanation
_________

given

=> a+b+c = 0___________(1)

and

=> a2+b2+c2 = 16________(2)

squaring the eq(1) we get

=>(a+b+c)2 = (0)2

=>a2+b2+c2+2ab+2bc+2ca = 0________(3)

by eq(2) and eq(3)

Now putting the value of "a2+b2+c2=16" in above equation we get,

=>2ab+2bc+2ca = -16

Taking 2 as common factor we get 

=>ab+bc+ca = -8_________answer

hope it will help you..