设x是根号下(3+根号5)- 根号下(3-根号5)的小数部分,y是根号下(6+3倍根号5)- 根号下(6-3倍根号5)的
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设x是根号下(3+根号5)- 根号下(3-根号5)的小数部分,y是根号下(6+3倍根号5)- 根号下(6-3倍根号5)的小数部分.求2/y-1/x
是我搞错了,不好意思,后面的是根号下(6+3倍根号3)- 根号下(6-3倍根号3)
是我搞错了,不好意思,后面的是根号下(6+3倍根号3)- 根号下(6-3倍根号3)
![设x是根号下(3+根号5)- 根号下(3-根号5)的小数部分,y是根号下(6+3倍根号5)- 根号下(6-3倍根号5)的](/uploads/image/z/8310035-11-5.jpg?t=%E8%AE%BEx%E6%98%AF%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%883%2B%E6%A0%B9%E5%8F%B75%EF%BC%89-+%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%883-%E6%A0%B9%E5%8F%B75%EF%BC%89%E7%9A%84%E5%B0%8F%E6%95%B0%E9%83%A8%E5%88%86%2Cy%E6%98%AF%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%886%2B3%E5%80%8D%E6%A0%B9%E5%8F%B75%EF%BC%89-+%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%886-3%E5%80%8D%E6%A0%B9%E5%8F%B75%EF%BC%89%E7%9A%84)
题目有问题,6-3√5 < 0,√(6 - 3√5)在实数范围内无意义.这里只做前一半,后一半请查清题目后接着问或仿照做.
设X = √(3+√5) - √(3 -√5)
X= √[(6+ 2√5)/2] - √[(6 - 2√5)/2]
= √[(5 + 2√5 + 1)/2] - √[(5- 2√5 + 1)/2]
= √[(√5 + 1)²/2] - √[(√5 - 1)²/2]
= (√5 + 1)/√2 - (√5 - 1)/√2
= (√5+ 1 - √5 + 1)/√2
= 2/√2 = √2
1 < X < 2
x = X - 1 = √2 - 1
1/x = 1/(√2 - 1) = (√2+ 1)/[(√2-1)(√2 + 1)] = √2 + 1
设X = √(3+√5) - √(3 -√5)
X= √[(6+ 2√5)/2] - √[(6 - 2√5)/2]
= √[(5 + 2√5 + 1)/2] - √[(5- 2√5 + 1)/2]
= √[(√5 + 1)²/2] - √[(√5 - 1)²/2]
= (√5 + 1)/√2 - (√5 - 1)/√2
= (√5+ 1 - √5 + 1)/√2
= 2/√2 = √2
1 < X < 2
x = X - 1 = √2 - 1
1/x = 1/(√2 - 1) = (√2+ 1)/[(√2-1)(√2 + 1)] = √2 + 1
设x是根号下(3+根号5)- 根号下(3-根号5)的小数部分,y是根号下(6+3倍根号5)- 根号下(6-3倍根号5)的
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