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  • 1 # 使用者9264775772483

    (1)解,得:ax^2+bx+c=0兩邊同除以a得x^2+(b/a)x+c/a=0x^2+b/ax+(b/2a)^2=(b/2a)^2-c/a(x+b/2a)^2=(b^2-4ac)/4a^2當b^2-4ac=0時x+b/2a=±(√b^2-4ac/2a)x=(-b±√b^2-4ac)/2a(2)解,得:x^2+4x+2=0X^2+4x+2=0x²+4x+x=2﹙x+2﹚²=2x+2=±√2x=-2±√2(3)解,得:(2x-1)^2=x(3x+2)-7(2 x - 1)² = x(3 x + 2)- 74 x ² - 4 x + 1 = 3 x ² + 2 x - 7x ² - 6 x + 8 = 0(x - 2)(x - 4)= 0x - 2 = 0 或 x - 4 = 0x₁ = 2 x₂ = 4(4)解,得:x^2-3x-2=0x^2-3x-2=0x^2-2*(3/2)x+(3/2)^2-(3/2)^2-2=0(x-3/2)^2=(3/2)^2+2(x-3/2)^2=9/4+2(x-3/2)^2=17/4x-3/2=±(√17)/2x=±(√17)/2+3/2x1=(√17)/2+3/2=(√17+3)/2x2=-(√17)/2+3/2=(-√17+3)/2(5)解,得:2x^2-5x+2=02x^2-5x+2=0x^2-5/2x+1=0x^2-5/2x+(5/4)^2 -(5/4)^2 +1=0(x-5/4)^2 =9/16x-5/4 =3/4或x-5/2 =-3/4x=2或x =1/2(6)x^2+根號3x-1=0(7)x^2-3x-1=0解,得:x²-3x=1x²-3x+﹙3/2﹚²=1+﹙3/2﹚²﹙x-3/2﹚²=13/4x-3/2=±√13/2x1=﹙3+√13﹚/2x2=﹙3-√13﹚/2(8)(x-3)^2=4x(x-3)解,得:x²-6x+9+4x²-12x=05x²-18x+9=0用公式x={-b±√(b^2-4ac)}/2a b²得:x1=3,x2=3\5(9)x^2-10x+9=0解,得:(x-1)(x-9)=0x=1或x=9(10)2x^2+1=3x解,得:2x^2-3x+1=0(2x-1)(x-1)=02x-1=0或x-1=0x1=1/2x2=1

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