Question

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

Answer 1

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