3x - 3y + 2z = 7
3x + 1y - 3z = -5 ⇒ 6x - 2y - 1z = 2 ⇒ 42x - 14y - 7z = 14
7x - 1y - 2z = 0 ⇒ 7x - 1y - 2z = 0 ⇒ 42x - 6y - 12z = 0 
 -20y - 19z = 14
 -20y + 20y - 19z = 14 + 20y
 -19z = 14 + 20y
 -19 -19
 z = -14/19 - 1 1/19y
 3x - 3y + 2(-14/19 - 1 1/19y) = 7
 3x - 3y - 1 9/19 - 2 2/19y = 7
 3x - 5 2/19y - 1 9/19 = 7
 +1 9/19 +1 9/19 
 3x - 5 2/19y = 8 9/19
 3x - 3x - 5 2/19y = 8 9/19 - 3x
 -5 2/19y = 8 9/19 - 3x
 -5 2/19 -5 2/19
 y = -1 64/97 + 57/97x
 3x - 3(-1 64/97 + 57/97x) + 2(-14/19 - 1 1/19y) = 7
 3x + 4 95/97 + 1 74/97x - 1 9/19 - 2 2/19y = 7
 4 74/97x - 2 2/19y + 3.5056972328 = 7
 -3.5056972328 -3.5056972328
 4 74/97x - 2 2/19y = 3.494302767
 4 74/97x + 2 2/19y - 2 2/19y = 3.494302767 + 22/19y
 4 74/97x = 3.494302767 + 2 2/19
 4 74/97 4 74/97
 x = 0.7336523126 + 0.4420141262y
3(0.733652316 + 0.4420141262y) - 3(-1 64/97 + 57/97x) + 2(-14/19 - 1 1/19y)=7
 2.200956948 + 1.326042379y + 4 95/97 - 1 74/97x - 1 9/19 - 2 2/19y = 7 -1 74/97x - 0.7792207789y + 5.706654181 = 7
 -5.706654181 -5.70665418
 -1 74/97x - 0.7792207789y = 1.293345820
(x, y, z) = (0.733652316 + 0.4420141262, -1 64/97 + 57/97x, -14/19 - 1 1/19y)

6 0

3 years ago

List all the possible rational zeros of p(x)=3x^3-3x^2+4x-12

skelet666 [1.2K]

Answer:

$x = 3$