计算:[3(x+b)^2-6(x+b)^2+9(x+b)]/[3(x+b)]-(x-b)^2;-学生作业帮-兵器谱
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计算:[3(x+b)^2-6(x+b)^2+9(x+b)]/[3(x+b)]-(x-b)^2;

来源:学生作业帮 编辑:作业帮 时间:2019/03/26 18:31:39

计算:[3(x+b)^2-6(x+b)^2+9(x+b)]/[3(x+b)]-(x-b)^2;

原式=3(x+b)³/[3(x+b)]-6(x+b)²/[3(x+b)]+9(x+b)/[3(x+b)]-(x-b)²
=x²+2bx+b²-2x-2b+3-x²+2bx-b²
=4bx-2x-2b+3

a平方-a -1=0 b平方-b-1=0
所以a和b是方程x2-x-1=0的根
由韦达定理
a+b=1
ab=-1
所以a2+b2=(a+b)2-2ab=3

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