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设x1x2是一元二次方程2²-5x+1=0的两个根,利用根和系数的关系,求下列式子的值:
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题中方程应该为:2x²+5x+1=0
x1+x2=5/2
x1×x2=1/2
①.(x1-3)(x2-3)=x1×x2-3(x1+x2)+9=5/2-3/2+9=1+9=0
②(x1+1)²+(x2+1)²=x1²+2x1+1+x2²+2x2+1
=x1²+x2²+2(x1+x2)+2
=(x1+x2)²-2x1x2+2(x1+x2)+2
=25/4-2×1/2+2×5/2+2
=25/4-1+5+2
=12又1/4
x1+x2=5/2
x1×x2=1/2
①.(x1-3)(x2-3)=x1×x2-3(x1+x2)+9=5/2-3/2+9=1+9=0
②(x1+1)²+(x2+1)²=x1²+2x1+1+x2²+2x2+1
=x1²+x2²+2(x1+x2)+2
=(x1+x2)²-2x1x2+2(x1+x2)+2
=25/4-2×1/2+2×5/2+2
=25/4-1+5+2
=12又1/4
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