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Question Number 162181 by bobhans last updated on 27/Dec/21

Solve the system of equations {: ((x^4 −2x+y=y^4 )),(((x^2 −y^2 )^3 = 3)) }

Solvethesystemofequationsx4−2x+y=y4(x2−y2)3=3}

Commented by benhamimed last updated on 27/Dec/21

(x^2 +y^2 )(x^2 −y^2 )−2x+y=0 (3)^(1/3) (x^2 +y^2 )−2x+y=0 x^2 +y^2 −(2/( (3)^(1/3) ))x+(1/( (3)^(1/3) ))y=0 (x−(1/( (3)^(1/3) )))^2 +(y+(1/(2(3)^(1/3) )))^2 =(1/( (6)^(1/3) ))+(1/(4(6)^(1/3) )) (x−((6)^(1/3) /3))^2 +(y+((6)^(1/3) /(12)))^2 =((5((36))^(1/3) )/(24)) les solution de system sont l ′ensemble des points qui forment un cercle (C) de centre (((6)^(1/3) /3);((−(6)^(1/3) )/(12))) et demi rayon (((√(30)).(6)^(1/3) )/(12))

(x2+y2)(x2−y2)−2x+y=033(x2+y2)−2x+y=0x2+y2−233x+133y=0(x−133)2+(y+1233)2=163+1463(x−633)2+(y+6312)2=536324lessolutiondesystemsontl′ensembledespointsquiformentuncercle(C)decentre(633;−6312)etdemirayon30.6312

Answered by cortano last updated on 28/Dec/21

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