一些二次根式已知4X^2+Y^2-4X-6Y+10=0,求(2/3X根号下9X+Y^2根号下X/Y^3)-(X^2根号下1/X-5X根号下Y/X)的值.已知根号下5约等于2.236,求(根号下80-根号下9/5)-(根号下16/5+4/5根号下45)的值.(结果精确到0.01)(1-2根

Question

一些二次根式
已知4X^2+Y^2-4X-6Y+10=0,求(2/3X根号下9X+Y^2根号下X/Y^3)-(X^2根号下1/X-5X根号下Y/X)的值.
已知根号下5约等于2.236,求(根号下80-根号下9/5)-(根号下16/5+4/5根号下45)的值.(结果精确到0.01)
(1-2根号下3)(1+2根号下3)-(2根号下3-1)^2的计算结果是_____(用最简二次根式表示)

Answer 1

4X^2+Y^2-4X-6Y+10=0
(4X^2-4X+1)+(Y^2-6Y+9)=0
(2X-1)^2+(Y-3)^2=0
平方大于等于0,相加等于0,若有一个大于0,则另一个小于0,不成立
所以两个都等于0
所以2X-1=0,Y-3=0
X=1/2,Y=3
[2/3X√(9X)+Y^2√(X/Y^3)]-[X^2√(1/X)-5X√(Y/X)]
=[1/3*√(9/2)+9*√(1/54)]-[(1/4)√2-5/2*√6]
=√2/2+√6/2-√2/4+5/2*√6
=√2/4+3√6
√5=2.236
[√80-√(9/5)]-[√(16/5)+4/5√45]
=4√5-3/5*√5-4/5*√5-12/5*√55
=0.2*√5
=0.2*2.236
=0.4472
(1-2√3)(1+2√3)-(2√3-1)^2
=1^2-(2√3)^2-[(2√3)^2-4√3+1]
=1-12-12+4√3-1
=-24+4√3