Question

if a+b=c ,then show that b^2+ac=c^2-ab

Answer 1

Given: a+b=c

$lhs = {b}^{2} + ac \\ from \: given \: b = c - a \\ so \: {b}^{2} = {c}^{2} + {a}^{2} - 2ac \\ substituting \: above \: we \: get \\ lhs = {c}^{2} + {a}^{2} - 2ac + ac \\ lhs = {c}^{2} + {a}^{2} - ac \\ lhs = {c}^{2 } + a(a - c) \\ lhs = {c}^{2} - ab \\ lhs = rhs \\ hence \: proved$