Question

已知：x的平方+x-1=0,求下列代数式的值

(1)2x的平方+2x-1; (2)x的平方+x的平方分之1; (3)x的3次方+2x的平方+1

Answer 1

∵x²+x-1=0
∴(x²+x-1)/x=0即x-1/x=-1
x²+x=1,
x³+x²-x=0即x³=x-x²
1)原式=2(x²+x)-1=2-1=1
2)x²+1/x²=(x-1/x）²+2=1+2=3
3）原式=x-x²+2x²+1
=x²+x+1
=1+1=2

Answer 2

x^2+x-1=0
x^2+x=1
2x^2+2x-1
= 2（x^2+x）-1
=2-1
=1

x^2+x-1=0
x+1-1/x=0
x-1/x=-1
x^2-2+1/x^2=1
x^2+1/x^2=3

x^3+2x^2+1
=x^3+x^2+x^2+1
=x(x^2+x)+x^2+1
=x+x^2+1
=x^2+x+1
=1=1
=2

Answer 3

x^2+x-1=0
x^2+x=1
2x^2+2x-1
= 2（x^2+x）-1
=2-1
=1

x^2+x-1=0
x+1-1/x=0
x-1/x=-1
x^2-2+1/x^2=1
x^2+1/x^2=3

x^3+2x^2+1
=x^3+x^2+x^2+1
=x(x^2+x)+x^2+1
=x+x^2+1
=x^2+x+1
=1=1
=2