Question

1.已知x=2/(√3)-1.求代数式x²-x+1的值 2.若x=√(2000X2001X2002X2003+1)-2001²,则x=?

Answer 1

1. x=2/(√3-1)=√3+1
x-1=√3
平方x²-2x+1=3
故x²-x+1=3+x=3+(√3+1)=4+√3
2. x=√(2000X2001X2002X2003+1)-2001²
=√[2001X2002X(2001-1)(2002-1)]-2001²
=√[(2001X2002)²-2X2001X2002+1]-2001²
=√(2001X2002-1)²-2001²
=2001X2002-1-2001²
=2001X(2002-2001)-1
=2001-1
=2000
希望能帮到你，祝学习进步O(∩_∩)O

Answer 2

1. x=2/(√3)-1=2(√3+1)/[(√3-1)(√3+1)]=√3+1，x-1=√3，所以x^2-x+1=x(x-1)+1=(√3+1)√3+1=3+√3+1=4+√3。
2. 设a=2000，则
x=√[a(a+1)(a+2)(a+3)+1]-(a+1)^2
=√{[a(a+3)][(a+1)(a+2)]+1}-(a+1)^2
=√[(a^2+3a)(a^2+3a+2)+1]-(a+1)^2
=√[(a^2+3a)^2+2(a^2+3a)+1]-(a+1)^2
=√(a^2+3a+1)^2-(a+1)^2
=(a^2+3a+1)-(a+1)^2
=(a^2+3a+1)-(a^2+2a+1)
=a
=2000.