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 $\le$ x2
+ y2
+ z2 $\le$ 150. Then, the
number of elements in the set S is equal to
______ .
Answer (integer)
8
Solution
$x - 2y + 5z = 0$ ....(1)<br><br>$- 2x + 4y + z = 0$ .....(2)<br><br>$- 7x + 14y + 9z = 0$ ....(3)<br><br>2.(1) + (2) we get z = 0, x = 2y<br><br>15 $\le$ 4y<sup>2</sup> + y<sup>2</sup> $\le$ 150<br><br>$\Rightarrow$ 3 $\le$ y<sup>2</sup> $\le$ 30<br><br>$$y \in \left[ { - \sqrt {30} , - \sqrt 3 } \right] \cup \left[ {\sqrt 3 ,\sqrt {30} } \right]$$<br><br>$y = \pm 2,\, \pm 3,\, \pm 4,\, \pm 5$<br><br>$\therefore$ no. of integer's in S is 8
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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