已知(3x-y)^2+|2x-y-3|=0,求5(2x-y)-2(6x-2y+2)+(4x-3y-二分之一)
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已知(3x-y)^2+|2x-y-3|=0,求5(2x-y)-2(6x-2y+2)+(4x-3y-二分之一)
∵(3x-y)²≥0,|2x-y-3|≥0
且(3x-y)²+|2x-y-3|=0
∴3x-y=0,2x-y-3=0
解得x=-3,y=-9
原式=10x-5y-12x+4y-4+4x-3y-1/2
=2x-4y-9/2
当x=-3,y=-9时
原式=2×(-3)-4×(-9)-9/2=51/2
以上为这种类型题目的标准答题过程,一定要掌握的~若不懂,
(3x-y)^2+|2x-y-3|=0
(3x-y)^2=0
|2x-y-3|=0
3x-y=0
2x-y-3=0
3x-2x=0-3
x=-3
y=3x
y=3*(-3)
y=-9
5(2x-y)-2(6x-2y+2)+(4x-3y-1/2)
=5[2*(-3)-(-9)] -2[6*(-3)-2*(-9)+2]+[4*(-3)-3*(-9)-1/2]
=5*(3)-2*(2)+14.5
=25.5
∵(3x-y)^2+|2x-y-3|=0,
∴3x-y=0 ①
2x-y-3=0 ②
①-② x+3=0 x=-3 则y=3x=-9
∴5(2x-y)-2(6x-2y+2)+(4x-3y-1/2)=10x-5y-12x+4y-4+4x-3y-1/2=2x-4y-9/2=2×(-3)-4×(-9)-9/2
=-6+36-9/2=51/2
(3x-y)^2>=0
|2x-y-3|>=0
所以
3x-y=0
2x-y=3
4x-3y=-3
将这三式代入所求式:
5*3-2*2+(-3-1/2)
=15-4-7/2
=15/2
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