Question

Himpunan penyelesaian SPLTV
2x- y+z=7
-x-2y+z=6
4x-2y-z=6
adalah ....... ....
nilai {x,y,z}
nilai x²+y²+z²=
tolong di bantu yahh

Answer 1

2x - y + z = 7 ... (1)
- x - 2y + z = 6 ... (2)
4x - 2y - z = 6 ... (3)

(1) dan (2)
2x - y + z = 7
- x - 2y + z = 6
____________ -
3x + y = 1 ... (4)

(2) dan (3)
- x - 2y + z = 6
4x - 2y - z = 6
_____________ +
3x - 4y = 12 ... (5)

(4) dan (5)
3x + y = 1
3x - 4y = 12
__________ -
5y = - 11
y = - 11/5
x = 16/15
- 16/15 + 22/5 + z = 6
z = 90/15 + 16/15 - 66/15
   = 40/15

x² + y² + z² = (16/15)² + (-33/15)² + (40/15)²
                 = (256 + 1089 + 1600)/225
                 = 2945/225