Question

ifa_b=3and b_c=5 the value of a2+b2+c2_ab_bc_ca is

Answer 1

a-b=3 -----(1)
b-c=5------(2)
a² + b² + c²-ab-bc-ca =??
a-b=3
squaring on both sides
(a-b)²=3²
a²+b²-2ab=9-------(3)
b-c=5
squaring on both sides
(b-c)² = 5²
b²+c²-2bc = 25-----(4)
add (1)&(2)

we get a-c=8
a-c=8
squaring on both sides
(a-c)² = 8²
a²+c²-2ac = 64------(5)
add (3),(4),(5)
a²+b²-2ab + b²+c²-2bc + a²+c²-2ac = 9+25+64
2a²+2b²+2c²-2ab-2bc-2ac=98
2(a²+b²+c²-ab-bc-ac)=98
a²+b²+c²-ab-bc-ca=98/2=49
a²+b²+c²-ab-bc-ca = 49