若/x一2/与/y一3/

Question

数学题、方程
若|x+2|与|y-3|互为相反数,且x-2y+z/2+5=1/2y+x+z.求z的平方-10的值.
已知关于x的方程1/2(1-x)=1+k的解与3/4(x-1)-2/5(3x+2)=1/10k-3/2(x-1)的解的和为零,求k的值.

Answer 1

|x+2|与|y-3|互为相反数
|x+2|+|y-3|=0
|x+2|=0
x=-2
|y-3|=0
y=3
x-2y+z/2+5=1/2y+x+z
5/2y+1/2z=5
(5/2 )x3+1/2z=5
1/2z=-5/2
z=-5
(-5)(-5)-10=15
(2)已知关于x的方程1/2(1-x)=1+k的解与3/4(x-1)-2/5(3x+2)=1/10k-3/2(x-1)的解的和为零,求k的值.
1/2(1-x)=1+k
1/2-1/2x=1+k
-1/2x=1/2+k
x=(1/2+k)(-2)
x=-1-2k
3/4(x-1)-2/5(3x+2)=1/10k-3/2(x-1)
3/4x-3/4-6/5x-4/5=1/10k-3/2x+3/2
(3/4-6/5+3/2)x=1/10k+(3/2+4/5+3/4)
21/20x=1/10k+61/20
x=2/21k+61/21
-1-2k+2/21k+61/21=0
(-42/21+2/21)k-21/21+61/21=0
-40/21k=-40/21
k=1