Let $(x, y, z)$ be points with integer coordinates satisfying the system of homogeneous equations:
$3x-y-z=0$ ...(i)
$- 3x + z = 0$ ...(ii)
$-3x+2y+z = 0$ ...(iii)
Then, the number of such points for which $x^2 + y^2+z^2 ≤100$, is
Answer & explanation
Correct answer: option 2
Adding (i) and (ii) equations, we get $y = 0$. From equation (ii), we have $z = 3x$.
It is given that $x^2 + y^2+z^2 ≤100$
$∴x^2 ≤10$
$⇒-\sqrt{10} ≤ x ≤ \sqrt{10}⇒ x=± 3, ±2, ±1, 0$ [∵ x is an integer]
Hence, there are 7 points.