X 3 + Y 3 + Z 3 = 33 Has A Solution In Z

     
(Spoiler: This answer contains the word “SEX”.) It depends. If you want three real numbers x,y,z satisfying x^3+y^3+z^3=33 then there are infinitely many, và they are very easy to lớn find. If ...

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If displaystylex+y+z=6 và displaystylex^2+y^2+z^2=14 & displaystylex^3+y^3+z^3=36 then what are displaystylex,y,z ?
displaystyleleftlbracex,y,z ight brace=leftlbrace1,2,3 ight brace Explanation: displaystyle1+2+3=6displaystyle1^2+2^2+3^2=1+4+9=14 ...
Yes, this can be solved without guessing, using Newton's identities . Since x + y + z = 0, they are the roots of t^3 + at -b = 0. Newton's identities give us (in a straightforward mechanical ...

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With some forethought, you can bring it down lớn one case to kiểm tra directly, which turns out lớn be a solution. A previous version of this answer examined the equation hack 7, which led to 16 cases ...
fMy; Solution:: Let x,y,z be the roots of an Cubic equation in terms of variable t So (t-x)cdot (t-y)cdot (t-z) = 0Rightarrow t^3-(x+y+z)t^2+(xy+yz+zx)t-xyz = 0 Now Given x+y+z=4;;,x^2+y^2+z^2=14;;, x^3+y^3+z^3=34 ...

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Using the surjectivity of pi_1(A,x_0) opi_1(X,x_0), one can show that every path in X between two points in A is homotopic to some path in A. This this end, let x and y be points in A ...
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