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共回答了20个问题采纳率:95% 举报
因为a^2+b^2+c^2-ab-3b-2c+4=0,(a^2+b^2/4-ab)+3(b^2/4-b+1)+(c^2-2c+1)=0,则(a-b/2)^2+3(b/2-1)^2+(c-1)^2=0,因为(a-b/2)^2≥0,(b/2-1)^2≥0,(c-1)^2≥0,所以a-b/2=0,b/2-1=0,c-1=0,则c=1,b=2,a=1,所以a+b+c=4.2、因式分解3x^3-7x^2+4=3x^3-6x^2-x^2+4=3x^2(x-2)-(x^2-4)=3x^2(x-2)-(x+2)(x-2)=(x-2)(3x^2-x-2)=(x-2)(3x+2)(x-1).x^4-4x+3=x^4-1-4x+4
=(x^2-1)(x^2+1)-4(x-1)
=(x^2+1)(x+1)(x-1)-4(x-1)
=(x-1)[(x^2+1)(x+1)-4]=(x-1)(x^3+x^2+x-3)
=(x-1)[(x^3-1) + (x^2-1)+(x-1)]
=(x-1)[(x-1)(x^2 + x +1)+(x-1)(x+1)+(x-1)]
=(x^2+2x+3)(x-1)^2.
3、证明:a=1995×1995+1995×1995×1996×1996+1996×1996
=1995×(1996-1)+1995×1995×1996×1996+1996×(1995+1)=1995×1996-1995+(1995×1996)^2+1996×1995+1996
=(1995×1996)^2+2×(1995×1996)+1
=(1995×1996+1)^2.即a是个完全平方数.因为a^2-3a+1=0,2a^5-5a^4+2a^3-8a^2+3a= 2a^3 (a^2 - 3a + 1) + a^4 - 8a^2 + 3a
= a^4 - 8a^2 + 3a
= a^2( a^2 -3a + 1) + 3a^3 - 9a^2 + 3a
= 3a^3 - 9a^2 + 3a
= 3a(a^2 -3a + 1)
=0.有不懂的地方欢迎追问,
1年前
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