If 8(a + b)3 + (a - b)3 = (3a + b) [Aa2 + Bb2 + Cb2), then what is the value of 2(A + B - C)?
Answer & explanation
Correct answer: option 3
8(a + b)3 + (a - b)3 = (3a + b) [Aa2 + Bb2 + Cb2)
x3 + y3 = (x + y) [x2 + y2 - xy]
x = 2(a + b)
y = (a - b)
⇒ (2a + 2b + a - b) [(2a + 2b)2 + (a - b)2 - 2(a + b) (a - b)] = (3a + b) [Aa2 + Bb2 + Cb2]
⇒ (3a + b) [(2a + 2b)2 + (a - b)2 - 2(a + b) (a - b)] = (3a + b) [Aa2 + Bb2 + Cb2]
⇒ (4a2 + 4b2 + 8ab + a2 + b2 - 2ab - 2a2 + 2b2) = [Aa2 + Bab + Cb2]
⇒ 3a2 + 7b2 + 6ab = Aa2 + Bab + Cb2
on comparing, A = 3, B = 6, C = 7
2(A + B - C) = 2(6 + 3 - 7) = 4