113x-y-z=0..............(1)
-3x+z=0..................(2)
-3x+2y+z=0..................(3)
y = 0 for all x & z
z = 3x
x2+y2+z2≤100
x2+0+(3x)2≤100
10x2≤100
x2≤10
x = 0,±1,±2,±3
y = 0,0,0,0
z = 0,±3,±6,±9
Hence , Ans : 7
Let (x,y,z) be points with integer coordinates satisfying th esystem o fhomogeneous equations
3x-y-z=0
-3x+z=0
-3x+2y+z=0
Then the number of such points for which x2+y2+z2≤100
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3 Answers
11