Mathematics (algebra) (X2-x+1)6=a0x12+a1x11+a2x10+… +a12, Ask for: (1) a0+a1+a2+… +a12 (2) a0+a2+a4+… +a12 Note: X is followed by the power, a is followed by the number in the lower right corner

Mathematics (algebra) (X2-x+1)6=a0x12+a1x11+a2x10+… +a12, Ask for: (1) a0+a1+a2+… +a12 (2) a0+a2+a4+… +a12 Note: X is followed by the power, a is followed by the number in the lower right corner

By algebraic method:
Substituting x = 1 into both ends of the equation, we have 1 = A0 + A1 + A2 + +a12
Substituting x = - 1 into both ends of the equation, then the sixth power of 3 = 729 = a0-a1 + A2-A3 + +a12
So 1 + 729 = 2 * (A0 + A2 + A4 +...) +a12);
So A0 + A1 + A2 + +a12=1;
a0+a2+a4+… +a12=365.