已知:已知:x²+x-1=0,试求x³+2x²+1999的值是多少?
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已知:已知:x²+x-1=0,试求x³+2x²+1999的值是多少?
已知:已知:x²+x-1=0,试求x³+2x²+1999的值是多少?
已知:已知:x²+x-1=0,试求x³+2x²+1999的值是多少?
x^3+2x^2+1999=x(x^2+x-1)+(x^2+x-1)+2000=2000
x²+x-1=0
所以
x²+x=1
所以
x³+x²=x
所以
x³+2x²+1999=x³+x²+x²+1999=x+x²+1999=1+1999=2000
x(x²+x-1)=0,则x^3+x^2=x.
x³+x²+x²+1999=x+x²+1999=1+1999=2000
x³+2x²+1999
=x³+x²-x+x²+x-1+2000
=x(x²+x-1)+(x²+x-1)+2000
=0+0+2000
=2000
x³+2x²+1999
=x³+x²-x+x²+x-1+2000
=x(x²+x-1)+(x²+x-1)+2000
=0+0+2000
=2000