Question

已知a-2b=5,则a^2-2ab-10b=? 若a+b=3，则ab+(a^2+b^2)/2=? 若4x^2+4xy+2y^2+6y+9=0,则x-y=?

Answer 1

1： a²－2ab－10b＝a（a－2b）－10b
＝5a－10b
＝5（a－2b）
＝5×5
＝25
2： ab＋（a²＋b²）/2＝（a＋b）²/2＝3²/2＝9/2.
3： 4x²＋4xy＋2y²＋6y＋9＝0
（4x²＋4x＋y²）＋（y²＋6y＋9）＝0
（2x＋y）²＋（y＋3）²＝0
y＋3＝0, y＝－3
2x＋y＝0, x＝3/2
x－y＝3/2＋3＝9/2.

Answer 2

解：
a-2b=5
a²-2ab-10b
=a(a-2b)-10b
=5a-10b
=5(a-2b)
=5×5
=25

a+b=3
ab+(a²+b²)/2
=(a²+2ab+b²)/2
=(a+b)²/2
=3²/2
=9/2

4x²+4xy+2y²+6y+9=0
4x²+4xy+y²+y²+6y+9=0
(x+2y)²+(y+3)²=0
y+3=0 y=-3
2x+y=0 x=3/2
x-y=3/2-(-3)=9/2

Answer 3

a-2b=5
a^2-2ab-10b
=a(a-2b)-10b
=5a-10b
=5(a-2b)
=5*5
=25

a+b=3
ab+(a^2+b^2)/2
=1/2(a^2+2ab+b^2)
=1/2(a+b)^2
=1/2*3
=3/2

4x^2+4xy+2y^2+6y+9=0
(2x+y)^2+(y+3)^2=0
(2x+y)^2=0
(y+3)^2=0
y=-3
2x=-y
x=-1/2y=3/2

x-y=3/2-(-3)=9/2

Answer 4

4.5