Let ( x , y , z ) be points with integer coordinates satisfying the system of homogeneous equations 3 x − y − z = 0 , − 3 x + z = 0 , − 3 x + 2 y + z = 0 . Then, the number of such points for which x

Question

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

TestHub · Accepted Answer

Given, 3 x − y − z = 0 and − 3 x + 2 y + z = 0 − 3 x + z = 0 ​ On adding Eqs. (i) and (ii), we get y = 0 So, 3 x = z Now, x 2 + y 2 + z 2 ≤ 100 ⇒ ⇒ ⇒ ∴ ​ x 2 + ( 3 x ) 2 + 0 ≤ 100 10 x 2 ≤ 100 x 2 ≤ 10 x = − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 ​ So, number of such 7 points are possible.

Mathematics - Determinant Question with Solution | TestHub

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JEE Main + Advanced (1 year 12th class)