已知a^2-a-1=0,求a^18+326/a^6的值
1个回答
题目是“已知a^2-a-1=0,求a^18+ 323 /a^6的值”吧?a^18+(323/a^6) =(a^2)^9+(323/(a^2)^3) =(a+1)^9+(323/(a+1)^3) =A^3+(323/A) =(A^4+323)/A 其中,A=(a+1)^3 根据已知条件：a^2-a-1=0 将其化为(a+1)^2-3(a+1)+1=0 即(a+1)^2=3(a+1)-1 (a+1)^3=3(a+1)^2-(a+1)=8(a+1)-3 即A=8(a+1)-3 A^2=64(a+1)^2-48(a+1)+9 =192(a+1)-64-48(a+1)+9 =144(a+1)-55 A^4=20736(a+1)^2-15840(a+1)+3025 =62208(a+1)-20736-15840(a+1)+3025 =46368(a+1)-17711 原式=(A^4+323)/A =(46368(a+1)-17711+323)/(8(a+1)-3) =(46368a+28980)/(8a+5) =5796(8a+5)/(8a+5) =5796
相关问题
