bai nay kho lem ban oi, moi cac ong ca ba cac anh cac chi vao day deeeeeeeeeee?

donna-marshall_60ca9808d321e

giai he phuong trinh

x^3+7x=y^3+7y

x^2+y^2=x+y+2

giai phuong trinh

x^2+xy+y^2-1=0

eden-morris_60ca980992790

x^3+7x=y^3+7y (1)

x^2+y^2=x+y+2 (2)

(1) <-> x^3 +7x- y^3-7y=0

x^3-y^3+ 7x-7y = 0

(x-y)(x^2+xy+y^2+7)=0

de thay (x^2+xy+y^2+7)>0 voi moi x,y ( vi x^2+xy+y^2+7 = (x+y/2)^2 +3y^2/4+7>0 )

vay x=y

thay vao (2) co

x^2+ x^2 = x +x +2

2x^2-2x-2=0

hay x^2-x-1=0

x=(1+can5)/2 va x=(1-can5)/2

2) giai pt x^2+xy+y^2-1=0 (1)

(1) <-> (x+y/2)^2 +3y^2/4=1 (4)

<-> 3x^2/4 +(x/2+y)^2 =1 (6)

tru hai ve cho nhau ta co

3/4(x^2-y^2) + (x/2+y)^2- (x+y/2)^2 =0

3/4(x-y)(x+y) +(y/2-x/2)( 3x/2+3y/2)=0

(x-y)(x+y)(3/4-3/2)=0

vay x=y va x= - y

thay vao (1)

x=y thi 3x^2=1 x= (+/-)can(1/3)

x= - y thi co x^2 = 1, x=+/-1, y= -/+1

thu lai thay dung