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Question Number 153698 by mathocean1 last updated on 09/Sep/21
solve in R { ((x^3 −y^3 =19)),((xy=6)) :}
solveinR{x3−y3=19xy=6
Answered by amin96 last updated on 09/Sep/21
(x−y)(x^2 +xy+y^2 )=19 ⇒ (x−y)((x−y)^2 +3xy)=19 (x−y)^3 +18(x−y)−19=0 ⇒ x−y=1 (x−y)((x+y)^2 −xy)=19 ⇒ (x+y)^2 =25 { ((x+y=±5)),((x−y=1 )) :} ⇒ { ((x+y=5)),((x−y=1)) :} ⇒ { ((x=3)),((y=2)) :} { ((x+y=−5)),((x−y=1)) :} ⇒ { ((x=−2)),((y=−3)) :} ⇒ answer (3; 2) (−2; −3)
(x−y)(x2+xy+y2)=19⇒(x−y)((x−y)2+3xy)=19(x−y)3+18(x−y)−19=0⇒x−y=1(x−y)((x+y)2−xy)=19⇒(x+y)2=25{x+y=±5x−y=1⇒{x+y=5x−y=1⇒{x=3y=2{x+y=−5x−y=1⇒{x=−2y=−3⇒answer(3;2)(−2;−3)
Answered by mr W last updated on 09/Sep/21
x^3 −((6/x))^3 =19 x^6 −19x^3 −216=0 x^3 =−8 or 27 ⇒x=−2 or 3 ⇒y=−3 or 2
x3−(6x)3=19x6−19x3−216=0x3=−8or27⇒x=−2or3⇒y=−3or2
Commented by mathocean1 last updated on 09/Sep/21
thanks sirs
thankssirs

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