If aligned & . array ccc a^2 & b^2 & c^2 (a+ )^2 & (b+ )^2 & (c+ ^2 ) (a- )^2 & (b- ^2 ) & (- ^2 . array ) &=k | array ccc a^2 & b^2 & c^2 a & b & c 1 & 1 & 1 array |, 0 aligned then k is equal to:

Step-by-step solution

Let = | array ccc a^2 & b^2 & c^2 (a+ )^2 & (b+ )^2 & (c+ )^2 (a- )^2 & (b- )^2 & (c- )^2 array | aligned & Apply R ₂ R ₂- R ₃ & = | array ccc a^2 & b^2 & c^2 (a+ )^2-(a- )^2 & (b+ )^2-(b- )^2 & (c+ )^2-(c- )^2 (a- )^2 & (b- )^2 & (c- )^2 array | &= | array ccc a^2 & b^2 & c^2 4 a & 4 b & 4 c (a- )^2 & (b- )^2 & (c- )^2 array | & ( (x+y)^2-(x-y)^2=4 x y ) & aligned Taking out 4 common from R ₂=4 | array ccc a^2 & b^2 & c^2 a & b & c a^2+ ^2-2 a & b^2+ ^2-2 b & c^2+ ^2-2 c array | aligned & Apply R ₃ [ R ₃- ( R ₁-2