Question

16. If a2 + b2 + c2 = 14, then ab + bc + ca is always

greater than or equal to

Answer 1

Let's a^2 be 2^2
b^2 be 3^2
c^2 be 1^2
4+9+1 = 14
4*9+9*1+1*4
36+9+4 = 49

It is greater than 14

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Answer 2

Thank you for asking this question, here is your answer.

a² + b² + c² = 14

In this situation we are aware of the fact that the square of every number is greater than or equal to 0.

now we will take the square of (a+b+c)

(a+b+c)²≥ 0

a² + b² + c²  + 2(ab + bc + ca) ≥ 0

14 +2 (ab + bc + ca) ≥ 0

2 (ab + bc + ca) ≥ - 14

ab  + bc + ca ≥ -14/2

ab + bc + ca ≥ - 7

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