Question

NO NGASAL!

Jika
x + y + 2z = k
x + 2y + z = k
2x + y + z = k

k ≠ 0

maka x² + y² + z² dalam k ialah ...

Answer 1

X + y + 2z = k
x + 2y + z = k
------------------ -
-y + z = 0

2x + y + z = k
-y + z = 0
------------------- -
2x + 2y = k

x + 2y + z = 2x + 2y
x + z = 2x
z = x

3x + y = k
x + (-y) = 0
------------------- +
4x = k
x = k/4
z = k/4

x + 2y + z = k
2(k/4) + 2y = k
k/2 + 2y = k
k/2 + 4y/2 = 2k/2
k + 4y = 2k
4y = 2k
y = 2k/4
y = k/2

()()()()()()()()

= x² + y² + z²
= 2(k/4(k/4)) + k/2(k/2)
= k/2(k/4) + k²/4
= k²/8 + k²/4
= k²/8 + 2k²/8
= 3k²/8

Maaf kalau salah