Question

5道数学题

1、根号2+根号3+根号5分之12=
2、1+根号2+根号3+根号6分之1=
3、解方程：X^2-(2-2根号2) X+3-2*根号2=0
4、解方程：（X+3）^2=(2X-5)^2
5、因式分解：X+Y-根号16X-根号64Y+20

Answer 1

1、12/(√2+√3+√5)
=12(√2+√3-√5)/[(√2+√3+√5)(√2+√3-√5)]
=12(√2+√3-√5)/[(√2+√3)^2-5]
=12(√2+√3-√5)/[5+2√6-5]
=12(√2+√3-√5)/(2√6)
=12*√6*(√2+√3-√5)/(2√6*√6)
=12*√6*(√2+√3-√5)/12
=√6*(√2+√3-√5)
=2√3+3√2-√30

2、1+根号2+根号3+根号6分之1
=1/(1+√2+√3+√6)
=1/(√2+√3+√6+1)
=(√2+√3-√6-1)/(√2+√3+√6+1)(√2+√3-√6-1)
=(√2+√3-√6-1)/[(√2+√3)^2-(√6+1)^2]
=(√2+√3-√6-1)/[5+2√6-(7+2√6)]
=(√2+√3-√6-1)/(-2)
=-(√2+√3-√6-1)/2
=(√6+1-√2-√3)/2

3、解方程：X^2-(2-2根号2) X+3-2*根号2=0
x^2-(2-2√2)x+3-2√2=0
x^2-2(1-√2)x+(1-√2)^2=0
[x-(1-√2)]^2=0
(x-1+√2)^2=0
x=1-√2

4、解方程：（X+3）^2=(2X-5)^2
(x+3)^2-(2x-5)^2=0
[(x+3)-(2x-5)][(x+3)+(2x-5)]=0
(x+3-2x+5)(x+3+2x-5)=0
(8-x)(3x-2)=0
x=8或x=2/3

5、差条件

因式分解：X+Y-根号16X-根号64Y+20
x+y-√16x-√64y+20
=x+y-4√x-8√y+20
=x-4√x+4+y-8√y+16
=(√x-2)^2+(√y-4)^2

Answer 2

3.79
4.55
-1，3-2根号2
2/3，8
（根号x-2)的平方+（根号y-4)的平方