化简√[5/2+√(9/4-√5)]

来源：学生作业帮助网编辑：作业帮时间：2024/11/15 12:14:41

化简√[5/2+√(9/4-√5)]
化简√[5/2+√(9/4-√5)]

化简√[5/2+√(9/4-√5)]
√(9/4-√5) = √[(1 - √5/2)^2] = √5/2 - 1
√[5/2+√(9/4-√5)] = √[5/2 + √5/2 - 1]
= √[(3 + √5)/2]
= (1/2)√(6 + 2√5)
= (1/2)√[(1 + √5)^2]
= (1 + √5)/2

√[5/2+√(9/4-√5)]
=√[5/2+√5/2-1]
=√[3/2+√5/2]
=1/2+√5/2