先化简,再求值:a^2-2a+1/a-1-根号a^2-2a+1/a^2-a 其中a=1/3+2根号2
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先化简,再求值:a^2-2a+1/a-1-根号a^2-2a+1/a^2-a 其中a=1/3+2根号2
a^2-2a+1/a-1-根号a^2-2a+1/a^2-a
=(a-1)^2/(a-1) - √(a-1)^2/a(a-1)
=(a-1)-(a-1)/a(a-1)
=a-1-1/a
∵a=1/3+2根号2
a=(3-2√2)/(9-8)=3-2√2
∴a-1-1/a
=3-2√2-1-1/(3-2√2)
=3-2√2-1-(3+2√2)
=-4√2-1
a^2-2a+1/a-1-根号a^2-2a+1/a^2-a
=(a-1)^2/(a-1) - √(a-1)^2/a(a-1)
=(a-1)-(a-1)/a(a-1)
=a-1-1/a
∵a=1/3+2根号2
a=(3-2√2)/(9-8)=3-2√2
∴a-1-1/a
=3-2√2-1-1/(3-2√2)
=3-2√2-1-(3+2√2)
=-4√2-1
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