Question

If a square+ b square+ c square=90, a+b+c=20 find the value of ab+bc+ca

Answer 1

Answer: ab + bc + ac = 155

Step-by-step explanation:

Given: a² + b² + c² = 90      and     a + b + c = 20

Square the second equation, subtract it from the first equation, then simplify.

Square the second equation:

(a + b + c)² = 20²

a² + b² + c² + 2ab + 2bc + 2ac = 400

Subtract the equations:

   a² + b² + c² + 2ab + 2bc + 2ac = 400

- (a² + b² + c²                                 = 90)

                         2ab + 2bc + 2ac = 310

Simplify:

2(ab + bc + ac) = 310

÷2                      ÷2    

  ab + bc + ac = 155