求解二次根式在实数范围内分解因式:√3 *x(4次)-√2 *x(x方-√2+1)+3*x(3次)+(√3-√6)x方+

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  • √3 *x(4次)-√2 *x(x方-√2+1)+3*x(3次)+(√3-√6)x方+x-√6

    =√3 *x^4-√2*x(x^2-√2+1)+3*x^3+(√3-√6)x^2+x-√6

    =√3 *x^4-√2*x^3+√2(√2-1)x+3*x^3+(√3-√6)x^2+x-√6

    =√3 *x^4+(3-√2)*x^3+(√3-√6)x^2+√2(√2-1)x+x-√6

    =√3 *x^4+(3-√2)*x^3+(√3-√6)x^2+(3-√2)x-√6

    =√3 *x^4+(√3-√6)x^2-√6 +(3-√2)*x^3+(3-√2)x

    =[√3 *x^2-√6][x^2+1]+(3-√2)*x[x^2+1]

    =√3[x^2-√2][x^2+1]+(3-√2)*x[x^2+1]

    =(x^2+1)[√3(x^2-√2)+(3-√2)*x]

    =(x^2+1)(√3x^2-√6+3x-√2x)

    =(x^2+1)(√3x^2-√6+3x-√2x)

    =(x^2+1)(√3x-√2)(x+√3)