Question

If a if a square + b square + c square is equal to 90 and a + b + c is equal to 20 then find the value of a b + bc + ca

Answer 1

(a+b+c) ^=a^+b^+c^+2(ab+bc+ca)
(20)^=90+2(ab+bc+ca)
400=90+2(ab+bc+ca)
400-90=2(ab+bc+ca)
310=2(ab+bc+ca)
310/2=ab+bc+ca
155=ab+bc+ca
I hope may be right

Answer 2

$(a + b + c) {}^{2} = a {}^{2} + b {}^{2} + c {}^{2} + 2ab + 2bc + 2ca...............(i) \\ \\ but \: given \: that \: a {}^{2} + b {}^{2} + c {}^{2} = 90 \\ \\ and \: \: a + b + c = 20 \\ \\ putting \: these \: values \: in \: equation \: (i) \\ \\ 20 {}^{2} = 90 + 2ab + 2bc + 2c \\ \\ 400 - 90 = 2(ab + bc + ca) \\ \\ ab + bc + ca = \frac{310}{2} \\ \\ = 155 \\ \\ \\ hope \: it \: helps....$