Question

Please answer this question



a + b + c = 12
a^2 + b^2 + c^2 = 64
Let ab + bc + ca​

Answer 1

Given, a+b+c=12

And a^2+b^2+c^2=64

We know that

(a+b+c) ^2

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

Hence,

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

2(ab+bc+ca)=(12)^2-(64)

2(ab+bc+ca)=144-64=80

(ab+bc+ca)=80/2=40

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Answer 2

a+b+c=12

Square both sides

(a+b+c)^2=12^2

Use identity

a^2+b^2+c^2+2(ab+bc+ca)=144

We have the value of a^2+b^2+c^2=64

So we will write it

64+2(ab+bc+ca)=144

2(ab+bc+ca)=144 - 64

2(ab+bc+ca)=80

(ab+bc+ca)=80/2

ab+bc+ca=40

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