已知x,y均为有理数,且满足√(9+4√2)=x+2√y,求立方根(2x-y)的值

2025-06-20 18:56:20
推荐回答(2个)
回答1:

9+4√2
=8+4√2+1
=(2√2+1)²
∴2√2+1=x+2√y
∵x,y均为有理数
∴x=1
y=2
∴2x-y=0
∴立方根(2x-y)=0

回答2:

√(9+4√2)
=√(8+(4√2)+1)
=√((2√2)²+2*2(√2)+1)
=√((2√2)+1)²
=(2√2)+1
√(9+4√2)=x+2√y
x=1
y=2
³√(2x-y)
=0