Question

if a+b+c=15 and a^2 +b^2+c^=65 hten find the value of ab+bc+ca

Answer 1

Answer:

Step-by-step explanation:

We have,

$a+b+c=15\: \: and \: \: {a}^{2}+ {b}^{2}+ {c}^{2}=65$

We know that,

$(a+b+c)^{2} =  {a}^{2} +  {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca$

$\implies (15)^{2} = 65 + 2(ab + bc + ca)$

$\implies 225 = 65 +  2(ab + bc + ca)$

$\implies 160 = 2(ab + bc + ca)$

$\implies (ab + bc + ca) = 80$