化简：x9+x8=x7+x6解：x9+x8−x7−x6=0x6(x3+x2−x−1)=0x6[x2(x+1)−(x+1)]=0x6(x+1)(x2−1)=0x6(x+1)2(x−1)=0∴x6=0或(x+1)2=0或x−1=0x1=x2=x3=x4=x5=x6=0x7=x8=−1x9=1\begin{aligned} &\text{化简：} \quad x^9 + x^8 = x^7 + x^6 \\ \\ &\text{解：} x^9 + x^8 - x^7 - x^6 = 0 \\ \\ &\quad \quad x^6 (x^3 + x^2 - x - 1) = 0 \\ \\ &\quad \quad x^6 \left[ x^2(x + 1) - (x + 1) \right] = 0 \\ \\ &\quad \quad x^6 (x + 1)(x^2 - 1) = 0 \\ \\ &\quad \quad x^6 (x + 1)^2 (x - 1) = 0 \\ \\ &\therefore \quad x^6 = 0 \quad \text{或} \quad (x + 1)^2 = 0 \quad \text{或} \quad x - 1 = 0 \\ \\ &\quad \quad x_1 = x_2 = x_3 = x_4 = x_5 = x_6 = 0 \\ \\ &\quad \quad x_7 = x_8 = -1 \\ \\ &\quad \quad x_9 = 1 \end{aligned}化简：x9+x8=x7+x6解：x9+x8−x7−x6=0x6(x3+x2−x−1)=0x6[x2(x+1)−(x+1)]=0x6(x+1)(x2−1)=0x6(x+1)2(x−1)=0∴x6=0或(x+1)2=0或x−1=0x1=x2=x3=x4=x5=x6=0x7=x8=−1x9=1