问题
解答题
若x1、x2是一元二次方程2x2-3x-1=0的两个根,求下列代数式的值. (1)
(2)x12+x22 (3)(x1-x2)2 (4)
(5)(x1-2)(x2-2) (6)(x1+
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答案
∵x1,x2是方程2x2-3x-1=0的两个根,
∴x1+x2=
,x1x2=-3 2
.1 2
(1)
+1 x1
=1 x2
=x1+x2 x1x2
=-3;3 2 - 1 2
(2)x12+x22=(x1+x2)2-2x1x2=(
)2-2×(-3 2
)=1 2
;13 4
(3)(x1-x2)2=(x1+x2)2-4x1x2=(
)2-4×(-3 2
)=1 2
;17 4
(4)
+x2 x1
=x1 x2
=
+x 21 x 22 x1x2
=-13 4 - 1 2
;13 2
(5)(x1-2)(x2-2)=x1x2-2(x1+x2)+4=-
-2×1 2
+4=3 2
;1 2
(6)(x1+
)(x2+1 x2
)=x1x2+2+1 x1
=-1 x1x2
+2+1 2
=-1 - 1 2
.1 2