<span>sinxcos2x-sin3x=0 ;
</span>sinxcos2x-sin(x+2x) =0 <span>;
</span>sinxcos2x-(sinxcos2x+sin2xcosx) =0 <span>;
</span>sinxcos2x- sinxcos2x - <span>sin2xcosx =0 ;
</span>- sin2xcosx =0 ;
sin2x =0 ⇒2x =π*k⇔ x=π*k/2 ;k<span>∈Z.
</span>cosx =0 ⇒x = π/2 +π*k ;k<span>∈Z.</span>
X*(x^2+2xy+y^2) / (x+y)*xy= x*(x+y)^2 / (x+y)*xy=(x+y) / y.
X²-2y=8
y+x²=2/3
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x²=8+2y
y+8+2y=(2/3)
3y=(2/3)-8
3y=-(22/3)
y=-(22/9)=-2*(4/9)
x²=8-2(22/9)
x²=8-(44/9)
x²=(72/9)-(44/9)
x²=(28/9)
x=((√28)/3)=(2(√7)/3)
Ответ: x=2(√7)/3; y=-2*4/9