If a (a + b + c)2 = 1792 b (a + b + c)2 = 1536 c (a + b + c)2 = 768,…

Add all the equations.

(a + b + c) (a + b + c)² = 1792 + 1536 + 768 = 4096

(a + b + c)³ = 4096

a + b + c = \(\sqrt[3]{4096}\)

a + b + c = 16

Now,

b (a + b + c)² = 1536

b (16)² = 1536

b = \(\frac{1536}{256}\) = 6

⇒ b² + 11 = 6² + 11 = 47