Question

If a + b + c is equals to 9, a b + BC + CA = 40 find a square + b square + c square

Answer 1

$a + b + c \: = 9$

$ab + bc + ca \: = 40$

Then,

$a ^{2} + b ^{2} + c ^{2}$

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

$(9) ^{2} = a ^{2} + b ^{2} + c ^{2} + 2(40)$

$81 = a ^{2} + b ^{2} + c ^{2} + 80$

$81 - 80 = a ^{2} + b ^{2} + c ^{2}$

$1 = a ^{2} + b ^{2} + c ^{2}$

$a ^{2} + b ^{2} + c ^{2} = 1$