Question

If (a+b+c)=15,(ab+bc+ca)=35 find a 2 +b 2 +c 2 .

Answer 1

squaring a + b + c = 15

[ (a + b) + c ]2 = 15 *15

(a+b)2 + 2 (a + b)*c + c2 = 225

a2 + 2ab + b2 + 2ac + 2bc + c2 = 225

a2 + 2 (ab + ac + bc ) + b2 + c2 = 225


Note: a + b + c = 15 and ab + bc + ac = 35


a2 + 2 (ab + ac + bc ) + b2 + c2 = 225

(a2 + b2 + c2) + 2 (ab + ac + bc) = 225

(a2 + b2 + c2) + 2 (35) = 225

a2 + b2 + c2 + 70= 225

a2 + b2 + b2 = 225 - 70

a2 + b2 + c2 = 155