chứng minh: `x^3-9x^2+30x-20+8y^3+12y^2+12y-12=(x-3)^3+(2y+1)^3+3(x+2y-2)`

Question

chứng minh: `x^3-9x^2+30x-20+8y^3+12y^2+12y-12=(x-3)^3+(2y+1)^3+3(x+2y-2)`

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Ximena 5 tháng 2021-07-11T09:06:12+00:00 2 Answers 7 views 0

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    0
    2021-07-11T09:07:14+00:00

    `#DyHungg`

    `x³-9x²+30x-20+8y³+12y²+12y-12`

    `=(x³-9x²+27x-27)+(8y³+12y²+6y+1)+(3x+6y-6)`

    `=(x-3)³+(2y+1)³+3(x+2y-2)`

    `⇒đpcm`

     

    0
    2021-07-11T09:07:27+00:00

    `VP=x³-9x²+30x-20+8y³+12y²+12y-12`

          `=x³-9x²+30x-32+8y³+12y²+12y`

          `=x³-9x²+27x+3x-27+1-6+8y³+12y²+6y+6y`

          `=(x³-9x²+27x-27)+(8y³+12y²+6y+1)+(3x+6y-6)`

          `=(x³-3.x².3+3.x.3²-3³)+[(2y)³+3.(2y)².1+3.2y.1²+1³]+3(x+2y-2)`

         `=(x-3)³+(2y+1)³+3(x+2y-2)`

    Vế phải bằng vế trái đẳng thức được chứng minh

     

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