Question

a square + b square + c square equal to 14 then a b + BC + CA is always greater than or equal to

Answer 1

it is always greater than equal
I hope it is correct

Answer 2

In this problem, we have a² + b² + c² = 14 ...............(1)

Again, we know that

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

so, a² + b² + c² + 2*(ab +bc +ca) ≥ 0 [ since, square of any real number can not be negative and so, (a + b + c)²≥0 ]

so, 2*(ab + bc + ca) + 14 ≥ 0 [ from (1)]

so, 2*(ab + bc + ca) ≥ -14

so, ab + bc + ca ≥ -7

Answer: (ab + bc + ca) is always greater than or equal to -7.