Let S be the set of all integer solutions x, y, z of the system of equations x-2 y+5 z=0 -2 x+4 y+z=0 -7 x+14 y+9 z=0 such that 15≤x^2+y^2+z^2≤150…

Question

Let S be the set of all integer solutions x, y, z of the system of equations x-2 y+5 z=0 -2 x+4 y+z=0 -7 x+14 y+9 z=0 such that 15≤x^2+y^2+z^2≤150. Then, the number of elements in the set S is equal to ..........

MARKS Content Team · Accepted Answer

Correct answer: 8. x-2y+5z=0 ...........i -2x+4y+z=0 ..........ii -7x+14y+9z=0 ..........iii Applying 2× equation i+equation ii, we get z=0 Putting z=0 in equation i, we get x=2y Given 15≤x^2+y^2+z^2≤150 ⇒15≤4y^2+y^2≤150 ⇒3≤y^2≤30 ⇒y=±2, ±3, ±4, ±5 ⇒8 solutions.

Let $S$ be the set of all integer solutions $(x, y, z)$ of the system of equations
$x - 2 y + 5 z = 0$
$- 2 x + 4 y + z = 0$
$- 7 x + 14 y + 9 z = 0$
such that $15 \leq x^{2} + y^{2} + z^{2} \leq 150$ . Then, the number of elements in the set $S$ is equal to ..........

Solution

Relevant Questions

Let S be the set of all integer solutions x, y, z of the system of equationsx-2 y+5 z=0-2 x+4 y+z=0-7 x+14 y+9 z=0such that 15≤x2+y2+z2≤150. Then, the number of elements in the set S is equal to ..........

Solution

Relevant Questions

Let $S$ be the set of all integer solutions $(x, y, z)$ of the system of equations
$x - 2 y + 5 z = 0$
$- 2 x + 4 y + z = 0$
$- 7 x + 14 y + 9 z = 0$
such that $15 \leq x^{2} + y^{2} + z^{2} \leq 150$ . Then, the number of elements in the set $S$ is equal to ..........