已知a^2=a+1求证a^5=5a+3

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已知a^2=a+1求证a^5=5a+3已知a^2=a+1求证a^5=5a+3已知a^2=a+1求证a^5=5a+3因为a^2=a+1所以a^5=(a^2)^2*a=(a+1)^2*a=(a^2+2a+

已知a^2=a+1求证a^5=5a+3
已知a^2=a+1求证a^5=5a+3

已知a^2=a+1求证a^5=5a+3
因为a^2=a+1
所以 a^5=(a^2)^2*a=(a+1)^2*a=(a^2+2a+1)*a=[(a+1)+2a+1]*a=(3a+2)*a=3a^2+2a=3(a+1)+2a=5a+3

a^4=(a^2)^2=(a+1)^2=a^2+2a+1=a+1+2a+1=3a+2
a^5=a^4*a=(3a+2)*a=3a^2+2a=3*(a+1)+2a=5a+3