If a, b and c are real numbers such that a^2+b^2+c^2-a b-b c-a c 0 , then | array ccc (a-b+1)^5 & b^7-c^7 & c^9-a^9 a¹¹-b¹¹ & (b-c+2)^3 & c¹³-a¹³ a¹⁵-b¹⁵ & b¹⁷-c¹⁷ & (c-a+3)^1 array |=

Step-by-step solution

Given, a^2+b^2+c^2-a b-b c-c a 0 1 2 [(a-b)^2+(b-c)^2+(c-a)^2 ] 0 It is possible only a=b=c aligned & Now, | array ccc (a-b+1)^5 & b^7-c^7 & c^9-a^9 a¹¹-b¹¹ & (b-c+2)^3 & c¹³-a¹³ a¹⁵-b¹⁵ & b¹⁷-c¹⁷ & (c-a+3) 1 array | & | array lll 1 & 0 & 0 0 & 8 & 0 0 & 0 & 3 array |=24 aligned