几道因式分解 用一元二次的应用2a^2-3a-12a^2-3ab-b^2-3p^2+4p+2x^2+49+600x^2-

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  • 2a^2-3a-1

    =2(a^2-3a/2)-1

    =2(a^2-3a/2+9/16)-1-18/16

    =2(a-3/4)^2-34/16

    =2[(a-3/4)^2-17/16]

    =2(a-3/4-√17/4)(a-3/4+√17/4)

    2a^2-3ab-b^2

    =2(a^2-3ab/2)-b^2

    =2(a^2-3ab/2+9b^2/16)-b^2-b^2/16

    =2(a-3b/4)^2-34b^2/16

    =2[(a-3b/4)^2-17b^2/16]

    =2(a-3b/4-b√17/4)(a-3b/4+b√17/4)

    -3p^2+4p+2

    =-3(p^2-4p/3)+2

    =-3(p^2-4p/3+4/9)+2+12/9

    =30/9-3(p-2/3)^2

    =3[10/9-(p-2/3)^2]

    =3(√10/3-p+2/3)(√10/3+p-2/3)

    x^2+49x+600

    =x^2+49x+2401/4-2401/4+600

    =(x+49/2)^2-1/4

    =(x+49/2-1/2)(x+49/2+1/2)

    =(x+24)(x+25)

    x^2-71x+300

    =x^2-71x+5041/4-5041/4+300

    =(x-71/2)^2-3841/4

    =(x+49/2-√3841/2)(x+49/2+√3841/2)

    6x^2-25x+24

    =(3x-8)(2x-3)

    8x^2-189x-72

    =(x-24)(8x+3)