谁能帮我看看这道题啊???不知道怎么解呢????
2个回答
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(1)
小李化简正确,√5>√2,√5-√2>0,因此算术平方根为√5-√2,而不是√2-√5
(2)
x=√(6-2√5)=√(1-2√5+5)=√(√5-1)²=√5-1
[1/(x-2) +1/(x+2)]·[(x²-4)/2(x-1)]
=[(x+2+x-2)/(x-2)(x+2)]·[(x²-4)/2(x-1)]
=[2x/(x²-4)]·[(x²-4)/2(x-1)]
=x/(x-1)
=(√5-1)/(√5-1-1)
=(√5-1)/(√5-2)
=(√5-1)(√5+2)/[(√5-2)(√5+2)]
=(3+√5)/(5-4)
=3+√5
小李化简正确,√5>√2,√5-√2>0,因此算术平方根为√5-√2,而不是√2-√5
(2)
x=√(6-2√5)=√(1-2√5+5)=√(√5-1)²=√5-1
[1/(x-2) +1/(x+2)]·[(x²-4)/2(x-1)]
=[(x+2+x-2)/(x-2)(x+2)]·[(x²-4)/2(x-1)]
=[2x/(x²-4)]·[(x²-4)/2(x-1)]
=x/(x-1)
=(√5-1)/(√5-1-1)
=(√5-1)/(√5-2)
=(√5-1)(√5+2)/[(√5-2)(√5+2)]
=(3+√5)/(5-4)
=3+√5
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