大师作文网关于因式分解的应用题,请求做,最快回答立即采纳
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关于因式分解的应用题,请求做,最快回答立即采纳
x^2-y^2+mx+5y-6
=x^2+mx-(y^2-5y+25/4)+25/4-6
=x^2+mx+1/4-(y^2-5y+25/4)
=x^2+mx+1/4-(y-5/2)^2
∴m=1时,多项式x^2-y^2+mx+5y-6能分解因式.
即：
x^2-y^2+x+5y-6
=x^2+x-(y^2-5y+25/4)+25/4-6
=x^2+x+1/4-(y^2-5y+25/4)
=x^2+x+1/4-(y-5/2)^2
=(x+1/2)^2-(y-5/2)^2
=(x+1/2+y-5/2)(x+1/2-y+5/2)
=(x+y-2)(x-y+3)
=x^2+mx-(y^2-5y+25/4)+25/4-6
=x^2+mx+1/4-(y^2-5y+25/4)
=x^2+mx+1/4-(y-5/2)^2
∴m=1时,多项式x^2-y^2+mx+5y-6能分解因式.
即：
x^2-y^2+x+5y-6
=x^2+x-(y^2-5y+25/4)+25/4-6
=x^2+x+1/4-(y^2-5y+25/4)
=x^2+x+1/4-(y-5/2)^2
=(x+1/2)^2-(y-5/2)^2
=(x+1/2+y-5/2)(x+1/2-y+5/2)
=(x+y-2)(x-y+3)