已知tana,tanb是方程7x^2-8x+1=0的两个根,求tan(a-b)_数学解答

已知tana,tanb是方程7x^2-8x+1=0的两个根,求tan(a-b)

人气：139 ℃　时间：2020-05-02 04:31:07

解答

tana+tanb=8/7
tanatanb=1/7
(tana-tanb)^2=(tana+tanb)-4tanatanb
=(8/7)^2-4/7
=64/49-28/49
=36/49
tana-tanb=±6/7
tan(a-b)=(tana-tanb)/(1+tanatanb)
=±6/7/(1+1/7)
=±6/(7+1)
=±6/8
=±3/4