Question

If a+b+c=15 and a 2 +b 2 +c 2 = 65 then find the value of ab+bc+ca

Answer 1

$a + b + c = 15 \\ Squaring \: both \: sides \\ (a +b+c)^2 = 15^2 \\ a^2+b^2+c^2+2ab+2bc+2ca =225 \\ 25 + 2ab + 2bc + 2ac = 225 \\ 25 + 2 ( ab + bc + ac ) = 225 \\ 2 ( ab + bc + ac ) = 225 - 25 \\ 2 ( ab + bc + ac ) = 200 \\ ab + bc + ac = \frac{200}{2} \\ ab + bc + ac = 100$

Answer 2

Answer:

ab+bc+ca=80

Step-by-step explanation:

a+b+c=15

If we do squaring on both sides

(a+b+c)²=15²

a²+b²+c²+2ab+2bc+2ca=225

65+2(ab+bc+ca)=225 {a²+b²+c²=65}

2(ab+bc+ca)=225-65

2(ab+bc+ca)=160

ab+bc+ca=160/2

ab+bc+ca=80