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[" Let "S" be the set of all integer sol...

[" Let "S" be the set of all integer solutions,"(x,y,z),],[" of the system of equations "],[x-2y+5z=0],[-2x+4y+z=0],[-7x+14y+9z=0],[" such that "15<=x^(2)+y^(2)+z^(2)<=150" .Then,the "],[" number of elements in the set "S" is equal to "]

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Let S be the set of all integer solutions, (x,y,z) of the system of equation x-2y+5z=0 -2x+14y + z=0 -7x+14 y + 9z =0 such that 15 le x^2 + y^2 + z^2 le 150 . Then, the number of elements of the set S is equal to ________

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