GIVEN :a2 + b2 + c2 + 84 = 4(a - 2b + 4c)Calculation :Rearranging the equation⇒ a2 + b2 + c2 + 84 - 4a + 8b -16c = 0⇒ a2 - 4a + 4 +b2 + 8b + 16+ c2 - 16c + 64 = 0⇒ (a – 2)2 + (b + 4)2 + (c-8)2 = 0IF (a - b)2 + (b – c)2+ (c - a)2 = 0Then a – b = 0⇒ a = b⇒ b = c⇒ c = a⇒ a = 2, b= -4, c = 8Then \([\sqrt {ab\; - \;bc + ca} ]\) =\([\sqrt {(2 \times - 4\;) - (8 \times - 4) + (8 \times 2)\;} ]\)\(\sqrt {( - 8) - ( - 32) + (16)\;} \) = \(\sqrt {40\;} \)⇒ \(\sqrt {{\bf{40}}\;} \) = 2\(\sqrt {{\bf{10}}} \) ∴\(\sqrt {ab - bc + ca} \) is EQUAL to 2\(\sqrt {{\bf{10}}} \)