合聚咖

合聚咖

(2014

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(1)∵AD平分∠BAC,

∴∠BAD=∠CAD,

∵DE∥AC,

∴∠CAD=∠ADE,

∴∠BAD=∠ADE,

∴AE=DE,

∵AD⊥DB,

∴∠ADB=90°,

∴∠EAD+∠ABD=90°,∠ADE+∠BDE=∠ADB=90°,

∴∠ABD=∠BDE,

∴DE=BE,

∵AB=5,

∴DE=BE=AE=

1
2
AB=2.5.

(2)原式=

2x(x?1)?(x?4)(x?6)
x(x?4)

=

x2?4x+24
x2?4x

∵x2-4x+1=0,∴x2-4x=-1,

原式=

?1+24
?1
=?23