If x2+x+1x2+2x+1=A+Bx+1+Cx+12, then A-B=
4
4C+1
3C
2
Explanation for the correct option:
x2+x+1x2+2x+1=A+Bx+1+Cx+12
Taking RHS
A+Bx+1+Cx+12=Ax+12+Bx+1+Cx+12=Ax2+2Ax+A+Bx+B+Cx2+2x+1=Ax2+2A+Bx+A+B+Cx2+2x+1
So,
x2+x+1x2+2x+1=Ax2+2A+Bx+A+B+Cx2+2x+1⇒x2+x+1=Ax2+2A+Bx+A+B+C
On comparing the coefficients, we get
A=1 and
2A+B=1⇒B=-1
Therefore, A-B=1+1=2
Hence. option D is correct.
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