題目有問題,6-3√5 < 0,√(6 - 3√5)在實數(shù)范圍內(nèi)無意義.這里只做前一半,后一半請查清題目后接著問或仿照做.
設(shè)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