Find a^2+b^2+c^2 when a+b+c=m and ab+bc+ca=n [S.Chand ICSE Class 9 Chapter 3 Exercise 3.1 Expansion and Factorisation Solution ]
(a+b+c)2 =a2+b2+c2+2(ab+bc+ca)
⟹ m2 = (a2+b2+c2) +2n [As a+b+c=m and ab+bc+ca=n ]
⟹ m2-2n = (a2+b2+c2)
Therefore, (a2+b2+c2) = m2– 2n
Similar Problem:
Find ab+bc+ca when a+b+c=12 and a2+b2+c2=50
a+b+c=12
∴ (a+b+c)2 =144
⟹ a2+b2+c2 +2(ab+bc+ca)=144
⟹ 50 + 2(ab+bc+ca)= 144
⟹ 2(ab+bc+ca)=144-50
⟹ 2(ab+bc+ca)=94
⟹ (ab+bc+ca) = $\frac{94}{2}$
⟹ (ab+bc+ca) = 47
∴ (ab+bc+ca) = 47 (Ans)