QJEEM20Ma28bc: JEE Main 2020 Mathematics - Class 12 JEEM20Ma28bc Solution: Let S be the set of all integer solutions, (x, y, z), of the…

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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 ______ .

Accepted Answer

x - 2y + 5z = 0

....(1)

- 2x + 4y + z = 0

.....(2)

- 7x + 14y + 9z = 0

....(3)

2.(1) + (2) we get z = 0, x = 2y

15

\le

4y² + y²

\le

150

\Rightarrow

3

\le

y²

\le

30

y \in \left[ { - \sqrt {30} , - \sqrt 3 } \right] \cup \left[ {\sqrt 3 ,\sqrt {30} } \right]

y = \pm 2,\, \pm 3,\, \pm 4,\, \pm 5

\therefore

no. of integer's in S is 8

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