Question

if a+b+c=12 and a square+ b square+ c square =100, find ab+bc+ca​

Answer 1

Answer:

22

Step-by-step explanation:

${(a + b + c)}^{2} = {12}^{2} =1 44 \\ \\ \\ \\ a + b + c = 12 \\ {(a + b + c)}^{2} = {12}^{2} =1 00 \\ {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca = 100 \\ \\ \\ \\1 00 + 2(ab + bc + ca) = 144 \\ \\ 2ab + 2bc + 2ca = 44 \\ \\ ab + bc + ca = 22$