Question

高一数学根式化简题 刚刚学习不太会做好心人帮忙

因为有根式 在word里截图了 图片可能在上传中 请耐心等待啊啊啊。感激不尽
如图

Answer 1

1. [(√2+2)/(a-2√a)+(1-√a)/(a-4√a+4)]÷(1-4/√a)-[(√a+2)/(a-4)]²
={(√2+2)/[√a(√a-2)]+(1-√a)/(√a-2)²}÷[(√a-4)/√a]-[(√a+2)/(a-4)]²
={(√2+2)(√a-2)/[√a(√a-2)^2]+(1-√a)√a/[√a(√a-2)^2]} × [√a/(√a-4)]-[(√a+2)/(a-4)]^2
觉得题目有些问题，你先看第二题吧

2.令t= [1+2√(7/3)/3]^(1/3)]+[1-2√(7/3)/3]^(1/3)]，则
t^3=[1+2√(7/3)/3]+[1-2√(7/3)/3]+3{ {[1+2√(7/3)/3]^2 × [1-2√(7/3)/3]} ^(1/3) + {[1+2√(7/3)/3] × [1-2√(7/3)/3]^2} ^(1/3) }
=2+3{ [1+2√(7/3)/3]^(1/3)]+[1-2√(7/3)/3]^(1/3)] × (-1/3)}
=2-t
=> t^3+t-2=0,
=> (t^2+t+2)(t-1)=0,
=> t=1
化简得1