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Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations: 3x – y – z = 0 -3x + z = 0 -3x + 2y + z = 0 Then the number of such points for which X 2 + y 2 + z 2 ≤ 100 is

Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations:
3x – y – z = 0
-3x + z = 0
-3x + 2y + z = 0
Then the number of such points for which
X2 + y2 + z2 ≤ 100 is

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
Sol. The given system of equation is
3x – y – z = 0
-3x + z = 0
-3x + 2y + z = 0
Let x = p where p is an integer
Then y = 0 anc z = 3p
But x2 + y2 + z2 ≤ 100 ⇒ p2 + 9 p2 ≤ 100
⇒ p2 ≤ 10 ⇒ p = 0, ± 1, ± 2 ± 3
i.e. Number of points (x, y, z) are 7.

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