Question

if a square + b square + c square is equal to 14 then a b + BC + AC is also greater than or equal to

Answer 1

a² + b²+c²=14

Now we have to find the value of a b + b c + c a

As we know, (a +b+c)²=a² + b²+c²+2 ( a b + b c + c a)

                                   = 14 + 2 ( a b + b c + c a)

 Since , (a +b+c)²≥0,⇒ Square of any real number is always ≥ 0.

So, 14 + 2 ( a b + b c + c a)≥ 0

    ⇒ 2 ( a b + b c + c a) ≥ 0 - 14

   ⇒  2 ( a b + b c + c a) ≥  - 14

    ⇒  a b + b c + c a ≥  - 14/2

   ⇒  a b + b c + c a  ≥ - 7