Edited by inhtoan, 14-06-2009 - 07:36.
giải pt nhưng bản chất lại là hpt!
Started By Kim Hue, 14-06-2009 - 02:00
#1
Posted 14-06-2009 - 02:00
$sin^{2} x +sin^{2} y +sin^{2} (x+y) = \dfrac{9}{4}$
#2
Posted 26-06-2009 - 07:01
<=>$\dfrac{1-cos2x}{2}+\dfrac{1-cos2y}{2}+1-cos^2(x+y)=\dfrac{9}{4}$$sin^{2} x +sin^{2} y +sin^{2} (x+y) = \dfrac{9}{4}$
<=>$\dfrac{cos2x+cos2y}{2}+cos^2(x+y)+\dfrac{1}{4}=0$
<=>$cos(x+y)cos(x-y)+cos^2(x+y)+\dfrac{1}{4}=0$
Dễ thấy $\Delta=cos^2(x-y)-1\le0$ =>để pt có nghiệm thì $cos(x-y)=1 or cos(x-y)=-1$
Xét $cos(x-y)=1=>cos(x+y)=\dfrac{-1}{2}$đưa về hệ pt
$cos(x-y)=-1=>cos(x+y)=\dfrac{1}{2}$ đưa về hệ pt
Edited by cvp, 26-06-2009 - 07:36.
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