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

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