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Find-all-set-of-ordered-triple-s-x-y-z-x-y-z-such-that-x-y-1-z-3-x-2-y-2-5-1-z-2-7-x-3-y-3-19-1-z-3-Please-show-your-solution-




Question Number 31286 by 6123 last updated on 05/Mar/18
Find all set of ordered triple/s (x,y,z),  x,y,z∈ℜ, such that  x−y=1−z  3(x^2 −y^2 )=5(1−z^2 )  7(x^3 −y^3 )=19(1−z^3 ).  Please show your solution.
Findallsetoforderedtriple/s(x,y,z),x,y,z,suchthatxy=1z3(x2y2)=5(1z2)7(x3y3)=19(1z3).Pleaseshowyoursolution.
Commented by 6123 last updated on 06/Mar/18
Thank you!!
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Answered by MJS last updated on 05/Mar/18
obviously all triples  (x,y,1) with x=y∈R solve the  given equations    3(x^2 −y^2 )=5(1−z)(1+z)  from (i): (1−z)=(x−y)  3(x−y)(x+y)=5(x−y)(1+z)  3(x+y)=5(1+z)  x=(5/3)(1+z)−y  into (i): (5/3)(1+z)−2y=1−z  y=(1/3)+(4/3)z  x=(4/3)+(1/3)z (from above)  into (iii):  7(((4/3)+(1/3)z)^3 −((1/3)+(4/3)z)^3 )=19−19z^3   z^3 −(7/2)z^2 +(7/2)z−1=0  (z−1)(z^2 −(5/2)z+1)=0  z_1 =1; z_2 =(1/2); z_3 =2  x_1 =(5/3); x_2 =(3/2); x_3 =2  y_1 =(5/3); y_2 =1; y_3 =3  so we have  (r;r;1) with r∈R  ((3/2);1;(1/2))  (2;3;2)
obviouslyalltriples(x,y,1)withx=yRsolvethegivenequations3(x2y2)=5(1z)(1+z)from(i):(1z)=(xy)3(xy)(x+y)=5(xy)(1+z)3(x+y)=5(1+z)x=53(1+z)yinto(i):53(1+z)2y=1zy=13+43zx=43+13z(fromabove)into(iii):7((43+13z)3(13+43z)3)=1919z3z372z2+72z1=0(z1)(z252z+1)=0z1=1;z2=12;z3=2x1=53;x2=32;x3=2y1=53;y2=1;y3=3sowehave(r;r;1)withrR(32;1;12)(2;3;2)
Commented by 6123 last updated on 06/Mar/18
Thank you!!!
Thankyou!!!

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