Menu Close

3-12-1-3-3-1-3-x-1-3-y-1-3-z-1-3-x-y-z-N-x-y-z-please-help-me-

Tinku Tara 0 Comments
Pin




Question Number 195855 by jabarsing last updated on 11/Aug/23
{ ((3(√(((12))^(1/3) −(3)^(1/3) ))=(x)^(1/3) +(y)^(1/3) −(z)^(1/3) )),((x,y,z ∈ N)) :} ⇒ x,y,z =? please help me
{3123−33=x3+y3−z3x,y,z∈N⇒x,y,z=?pleasehelpme
Answered by Rasheed.Sindhi last updated on 13/Aug/23
Unsuccessful Try... { ((3(√(((12))^(1/3) −(3)^(1/3) ))=(x)^(1/3) +(y)^(1/3) −(z)^(1/3) )),((x,y,z ∈ N)) :} ⇒ x,y,z =? (3(√(((12))^(1/3) −(3)^(1/3) )))^3 =((x)^(1/3) +(y)^(1/3) −(z)^(1/3) )^3 (a+b−c)^3 =a^3 +b^3 −c^3 +3ab(a+b)−3bc(b−c)−3ac(a−c)−6abc 27(√((((12))^(1/3) −(3)^(1/3) )^3 )) =x+y−z+3((xy))^(1/3) ((x)^(1/3) +(y)^(1/3) ) −3((yz))^(1/3) ((y)^(1/3) −(z)^(1/3) ) −3((xz))^(1/3) ((x)^(1/3) −(z)^(1/3) ) −6((xyz))^(1/3) (a−b)^3 =a^3 −b^3 −3ab(a−b) LHS: 27(√(12−3−3((36))^(1/3) (((12))^(1/3) −(3)^(1/3) ))) =27(√(9−((36))^(1/3) (((12))^(1/3) −(3)^(1/3) ))) =27(√(9−((36))^(1/3) (3)^(1/3) ((4)^(1/3) −1 ))) =27(√(9−3(4)^(1/3) ((4)^(1/3) −1 ))) =27(√(9−6(2)^(1/3) −3(4)^(1/3) )) (LHS)^2 =729(9−6(2)^(1/3) −3(4)^(1/3) ) RHS: =x+y−z+3((xy))^(1/3) ((x)^(1/3) +(y)^(1/3) ) −3((yz))^(1/3) ((y)^(1/3) −(z)^(1/3) ) −3((xz))^(1/3) ((x)^(1/3) −(z)^(1/3) ) −6((xyz))^(1/3) (RHS)^2 =(x+y−z+3((xy))^(1/3) ((x)^(1/3) +(y)^(1/3) ) −3((yz))^(1/3) ((y)^(1/3) −(z)^(1/3) ) −3((xz))^(1/3) ((x)^(1/3) −(z)^(1/3) ) −6((xyz))^(1/3) )^2 (LHS)^2 =(RHS)^2 Too complicated .....
UnsuccessfulTry…{3123−33=x3+y3−z3x,y,z∈N⇒x,y,z=?(3123−33)3=(x3+y3−z3)3(a+b−c)3=a3+b3−c3+3ab(a+b)−3bc(b−c)−3ac(a−c)−6abc27(123−33)3=x+y−z+3xy3(x3+y3)−3yz3(y3−z3)−3xz3(x3−z3)−6xyz3(a−b)3=a3−b3−3ab(a−b)LHS:2712−3−3363(123−33)=279−363(123−33)=279−36333(43−1)=279−343(43−1)=279−623−343(LHS)2=729(9−623−343)RHS:=x+y−z+3xy3(x3+y3)−3yz3(y3−z3)−3xz3(x3−z3)−6xyz3(RHS)2=(x+y−z+3xy3(x3+y3)−3yz3(y3−z3)−3xz3(x3−z3)−6xyz3)2(LHS)2=(RHS)2Toocomplicated…..

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *