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Diketahui m = ⎝ ⎛ ​ 4 3 − 2 ​ ⎠ ⎞ ​ dan n = ⎝ ⎛ ​ 2 − 1 p ​ ⎠ ⎞ ​ . Jika ∣ ∣ ​ 2 m + n ∣ ∣ ​ = 5 6 ​ , tentukanlah nilai .

Diketahui  dan . Jika , tentukanlah nilai p.

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

nilai atau

nilai p equals negative 1 atau p equals 9 

Pembahasan

Diketahui dan . Jika , maka: Sehingga: Jadi, nilai atau

Diketahui m with rightwards arrow on top equals open parentheses table row 4 row 3 row cell negative 2 end cell end table close parentheses dan n with rightwards arrow on top equals open parentheses table row 2 row cell negative 1 end cell row p end table close parentheses. Jika open vertical bar 2 m with rightwards arrow on top plus n with rightwards arrow on top close vertical bar equals 5 square root of 6, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 m with rightwards arrow on top plus n with rightwards arrow on top end cell equals cell 2 open parentheses table row 4 row 3 row cell negative 2 end cell end table close parentheses plus open parentheses table row 2 row cell negative 1 end cell row p end table close parentheses end cell row blank equals cell open parentheses table row 8 row 6 row cell negative 4 end cell end table close parentheses plus open parentheses table row 2 row cell negative 1 end cell row p end table close parentheses end cell row blank equals cell open parentheses table row cell 8 plus 2 end cell row cell 6 plus left parenthesis negative 1 right parenthesis end cell row cell negative 4 plus p end cell end table close parentheses end cell row blank equals cell open parentheses table row 10 row 5 row cell negative 4 plus p end cell end table close parentheses end cell end table 

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 2 m with rightwards arrow on top plus n with rightwards arrow on top close vertical bar end cell equals cell square root of 10 squared plus 5 squared plus left parenthesis negative 4 plus p right parenthesis squared end root end cell row cell 5 square root of 6 end cell equals cell square root of 125 plus left parenthesis negative 4 plus p right parenthesis squared end root end cell row cell open parentheses 5 square root of 6 close parentheses squared end cell equals cell open parentheses square root of 125 plus left parenthesis negative 4 plus p right parenthesis squared end root close parentheses squared end cell row 150 equals cell 125 plus left parenthesis negative 4 plus p right parenthesis squared end cell row 25 equals cell left parenthesis negative 4 plus p right parenthesis squared end cell row cell plus-or-minus 5 end cell equals cell negative 4 plus p end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 4 plus p end cell equals 5 row p equals cell 5 plus 4 end cell row p equals 9 end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 4 plus p end cell equals cell negative 5 end cell row p equals cell negative 5 plus 4 end cell row p equals cell negative 1 end cell end table 

Jadi, nilai p equals negative 1 atau p equals 9 

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