已知x1、X2为方程x²+3x+1=0的两实数根, - 知识问答

已知x1、X2为方程x²+3x+1=0的两实数根,则x1³+8x2+20=?

3个回答

x1²+3x1+1=0
x1²=-1-3x1
x1+x2=-3
x1³+8x2+20
=x1*x1²+8x2+20
=x1(-1-3x1)+8x2+20
=-3x1²-x1+8x2+20
=-3(-1-3x1)-x1+8x2+20
=8x1+8x2+23
=8(x1+x2)+23
=8(-3)+23
=-1

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