Tentukan HP : 1/x + 1/y + 1/z = 1/4 1/x + 1/z = 1/6 1/y + 1/z = 1/8
Matematika
nauval78
Pertanyaan
Tentukan HP :
1/x + 1/y + 1/z = 1/4
1/x + 1/z = 1/6
1/y + 1/z = 1/8
1/x + 1/y + 1/z = 1/4
1/x + 1/z = 1/6
1/y + 1/z = 1/8
1 Jawaban
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1. Jawaban ahreumlim
misalkan
m = 1/x
n = 1/y
p = 1/z
maka sistem dapat ditulis
m + n + p = 1/4 ..............(1)
m + p = 1/6 ..............(2)
n + p = 1/8 ..............(3)
dari (1) dan (2)
m + n + p = 1/4
m + p = 1/6 -
------------------------
n = 1/4 - 1/6
n = 6/24 - 4/24
n = 2/24
subtitusikan nilai n = 2/24 ke pers. (3)
n + p = 1/8
2/24 + p = 1/8
p = 3/24 - 2/24
p = 1/24
subtitusikan nilai p = 1/24 ke pers. (2)
m + p = 1/6
m + 1/24 = 4/24
m = 3/24
Jadi
m = 3/24
1/x = 3/24
x = 24/3
x = 8
n = 2/24
1/y = 2/24
y = 24/2
y = 12
p = 1/24
1/z = 1/24
z = 24
Jadi HP : {(8, 12, 24)}