1、m-n=2,mn=1,则m^4 n^2+m^2 n^4的值是（） 2、分解因式：(x^2-xy)^2-(xy-y^2
2个回答
1.mn=1→m²n²=1
m－n=2→(m－n)²=4
m^4·n²＋m²n＾4
=m²n²(m²＋n²)
=m²n²[(m－n)²＋2mn]
=1×(4＋2×1)
=6
2.(x^2-xy)^2-(xy-y^2)^2=(x²－xy－xy＋y²)(x²－xy＋xy－y²)
=(x²－2xy＋y²)(x²＋y²)
=(x＋y)²(x²－y²)
=(x＋y)²(x＋y)(x－y)
=(x＋y)³(x－y)
3.a²－3a＋1=0
两边同时除以a
→a－3＋1/a=0
→a＋1/a=3
(a＋1/a)²=9
→a²＋2＋1/a²=9
→a²＋1/a²=7
4.无图?
5.2x＋3y-4=0
→3y=－2x＋4
两边同时除以3
→y=－2/3x＋4/3
∴k=－2/3
6.(1)4－x^2－4xy－4y^2
=－x²－4xy－4y²＋4
=－(x＋2y)²＋4
=(4－x－2y)(4＋x＋2y)
(2)a^2＋2a(b＋c)＋(b＋c)^2
=[(a＋(b＋c)]²
=(a＋b＋c)²
(3) (x^2－5)^2＋8(x^2－5)＋16
=[(x²－5)＋4]
=(x－1)²
(4)16(m－n)^2－9(m＋n)^2
=[4(m－n)－3(m＋n)][4(m－n)＋3(m＋n)]
=(4m－4n－3m－3n)(4m－4n＋3m＋3n)
=(m－7n)(7m－n)
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