Paragraph: Let a , b and c be three real numbers satisfying [ array lll a & b & c array ] [ array lll 1 & 9 & 7 8 & 2 & 7 7 & 3 & 7 array ]= [ array lll 0 & 0 & 0 array ] Question: Let be a solution of x^3-1=0 with Im ( )>0 . If a=2 , with b and c satisfying Eq. (E), then the value of 3 ^a + 1 ^b + 3 ^c

Step-by-step solution

aligned & Given, [a b c]_ 1 3 [ array lll 1 & 9 & 7 8 & 2 & 7 7 & 3 & 7 array ]_ 3 3 = [ array lll 0 & 0 & 0 array ] & [ array c a+8 b+7 c 9 a+2 b+3 c 7 a+7 b+7 c array ]= [ array l 0 0 0 array ] & a+8 b+7 c=0 & 9 a+2 b+3 c=0 & a+b+c=0 & aligned On multiplying Eq. (iii) by 2 , then subtract from Eq. (ii), we get 7 a+c=0 Again multiplying Eq. (iii) by 3 , then subtract from Eq. (ii), we get array ll & 6 a-b=0 & b=6 a and c=-7 a array If a=2, b=12 and c=-14 aligned & 3 ^a + 1 ^b + 3 ^c & 3 ^2 + 1 ¹² + 3 ⁻¹⁴ = 3 ^2 +1