Question

已知x1、x2是方程x²+3x+1=0的两实数根,则x1³+8x2+20等于多少

Answer 1

x1、x2是方程是根，则：(x1)²＋3(x1)＋1=0，即：(x1)²=－3(x1)－1且x1＋x2=－3
x1³＋8x2＋20
=x1(x1)²＋8x2＋20
=x1(－3x1－1)＋8x2＋20
=－3(x1)²－x1＋8x2＋20
=3[3x1＋1]－x1＋8x2＋20
=8x1＋8x2＋23
=8(x1＋x2)＋23
=－24＋23
=－1

Answer 2

x1、x2是方程是根，则：(x1)²＋3(x1)＋1=0，即：(x1)²=－3(x1)－1且x1＋x2=－3
x1³＋8x2＋20
=x1(－3x1－1)＋8x2＋20
=－3(x1)²－x1＋8x2＋20
=3[3x1＋1]－x1＋8x2＋20
=8x1＋8x2＋23
=8(x1＋x2)＋23
=－24＋23
=－1
答的因该是这样，请纳用。