Toán Lớp 11: 2cos2x + tanx= 4/5 ( giải PT )

Question

Toán Lớp 11:  2cos2x + tanx= 4/5 ( giải PT )

mocmien87 · Answer

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maitrucloan · Answer

$2 cos 2x+ tan x= dfrac45$     Điều kiện $ cos x ne0 Leftrightarrow x ne dfrac{ pi}2+k pi$ $(k in mathbb Z)$     Phương tr&igrave;nh tương đương:     $2.(2 cos&sup2;x -1)+ tan x= dfrac45$     $ Leftrightarrow4 cos&sup2;x -2 +  tan x - dfrac45=0$     $ Leftrightarrow  dfrac{4}{ tan&sup2;x +1} + tan x - dfrac{14}5=0$     $ Leftrightarrow4 +  tan x.(  tan&sup2;x +1) - dfrac{14.( tan&sup2;x+1)}{5}=0$     $ Leftrightarrow 20 +5. tan x.( tan&sup2;x+1) -14.( tan&sup2;x+1)=0$     $ Leftrightarrow 20 +5 tan&sup3;x +5 tan x -14 tan&sup2;x -14=0$     $ Leftrightarrow 5 tan&sup3;x -14 tan&sup2;x +5 tan x +6=0$      ( Leftrightarrow left[  begin{array}{l} tan x =2   tan x= dfrac{2- sqrt{19}}5   tan x= dfrac{2+ sqrt{19}}5 end{array}  right. )       ( Leftrightarrow left[  begin{array}{l} x = arctan2+k pi   x= arctan dfrac{2- sqrt{19}}5+k pi   x= arctan dfrac{2+ sqrt{19}}5+k pi end{array}  right. ) $(k in mathbb Z)$ (thỏa m&atilde;n)     Vậy phương tr&igrave;nh c&oacute; nghiệm l&agrave;      ( left {  begin{array}{l} x = arctan2+k pi   x= arctan dfrac{2- sqrt{19}}5+k pi   x= arctan dfrac{2+ sqrt{19}}5+k pi end{array}  right. ) $(k in mathbb Z)$