hbjihao
幼苗
共回答了20个问题采纳率:75% 举报
①已知(2x+y)/3-(3x-y)/2=0,求x2-y2的值
(2x+y)/3-(3x-y)/2=0
2(2x+y)-3(3x-y)=0
-5x+5y=0
x-y=0
x^2-y^2=(x+y)(x-y)=0
②1÷{(a-b)/(a-c)÷[(b-a)/(b-c)÷(c-a)/(c-b)]}
=1÷{(a-b)/(a-c)÷[(b-a)/(a-c)]}
=1÷(-1)
=-1
③3(x-y)=4y+6
3x-7y=6 1)
(x-y)/3-(x+y)/4=-1
4(x-y)-3(x+y)=-12
x-7y=-12 2)
1)-2),得
x=9
y=3
④若2x的2m+3次方+3y的5n-7次方=4是关于x、y的二元一次方程,求m2+n的值.
2x^(2m+3)+3y^(5n-7)=4
2m+3=1
5n-7=1
m=-1,n=8/5
m^2+n=1+8/5=13/5
⑤3(x-y)=4y+6
3x-7y=6 1)
(x-y)/3-(x+y)/4=-1
4(x-y)-3(x+y)=-12
x-7y=-12 2)
1)-2),得
x=9
y=3
⑥.已知:(x+1)/2=(y+3)/4=(x+y)/5,求(3x+2y+1)/(x+2y+3)的值.
(3x+2y+1)/(x+2y+3)
=[(x+1)+2(x+y)]/[(x+y)+(y+3)]
=(2+2*5)/(5+4)
=4/3
(解出x=7,y=13代入原式也行)
⑦.已知(方程组) 4x-3y-6z=0,x+2y-7z=0,求(2x2+3y2+6z2)/(x2+5y2+7z2)的值.
4x-3y-6z=0 1)
x+2y-7z=0 2)
1)-2)×4),得-11y+22z=0,y=2z
代入2),得x=3z
所以x:y:z=3:2:1
(2x2+3y2+6z2)/(x2+5y2+7z2)
=(18+12+6)/(9+20+7)
=1
⑧.先化简,后求值.(x-2y)2-(2x-y)2+[(xy+2)(xy-2)-2x2y2+4]÷xy,其中x=10,y=-1/5
(x-2y)2-(2x-y)2+[(xy+2)(xy-2)-2x2y2+4]÷xy
=(x-2y+2x-y)(x-2y-2x+y)+[(x^2y^2-4-2x^2y^2+4]÷xy
=(3x-3y)(-x-y)+(-x^2y^2)÷xy
=-3(x^2-y^2)-xy
=-3(100-1/25)+2
=-297.88
⑨(m+3)/3-(n-m)/4=-1/3
4(m+3)-3(n-m)=-4
7m-3n=-16 1)
4m+3/4n=-7/4
16m+3n=-7 2)
1)+2),得23m=-23,m=-1
代入1),得n=3
⑩.若x2-4x+1=0,求下列代数式的值.(1)x+1/x (2)x2+1/x2
因为x=0不是原方程的解,所以等式两边可以同时除以x
x-4+1/x=0
x+1/x=4
x^2+1/x^2=(x+1/x)^2 -2=4^2 -2=14
若关于x,y的方程组x+2y=5k x-y=9k ,的解适合方程3x+2y=17,求k的值.
设3x+2y=a(x+2y)+b(x-y)
那么a+b=3,2a-b=2
得a=5/3,b=4/3
17=5k*(5/3)+9k*(4/3)=61k/3
k=51/61
1年前
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