Diketahui ∣a∣=3​, ∣∣​b∣∣​=1, ∣∣​a−b∣∣​=1, maka nilai ∣∣​a+b∣∣​=...

Pertanyaan

Diketahui open vertical bar a with bar on top close vertical bar equals square root of 3 comma space open vertical bar b with bar on top close vertical bar equals 1 comma space open vertical bar a with bar on top minus b with bar on top close vertical bar equals 1, maka nilai open vertical bar a with bar on top plus b with bar on top close vertical bar equals... 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style open vertical bar straight a with bar on top plus straight b with bar on top close vertical bar equals square root of 7 end style

Pembahasan

Perhatikan bahwa begin mathsize 14px style open vertical bar straight a plus-or-minus straight b close vertical bar equals square root of open vertical bar straight a close vertical bar squared plus open vertical bar straight b close vertical bar squared plus-or-minus 2 open vertical bar straight a close vertical bar times open vertical bar straight b close vertical bar times cos space straight theta end root end style. Sehingga 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight a minus straight b close vertical bar end cell equals cell square root of open vertical bar straight a close vertical bar squared plus open vertical bar straight b close vertical bar squared minus 2 times open vertical bar straight a close vertical bar times open vertical bar straight b close vertical bar times cos space straight theta end root end cell row 1 equals cell square root of open parentheses square root of 3 close parentheses squared plus open parentheses 1 close parentheses minus 2 times open vertical bar straight a close vertical bar times open vertical bar straight b close vertical bar times cos space straight theta end root end cell row 1 equals cell square root of 3 plus 1 minus 2 times open vertical bar straight a close vertical bar times open vertical bar straight b close vertical bar times cos space straight theta end root end cell row 1 equals cell square root of 4 minus 2 times open vertical bar straight a close vertical bar times open vertical bar straight b close vertical bar times cos space straight theta end root end cell row cell open parentheses 1 close parentheses squared end cell equals cell open parentheses square root of 4 minus 2 times open vertical bar straight a close vertical bar times open vertical bar straight b close vertical bar times cos space straight theta end root close parentheses squared end cell row 1 equals cell 4 minus 2 times open vertical bar straight a close vertical bar times open vertical bar straight b close vertical bar times cos space straight theta end cell row cell 2 times open vertical bar straight a close vertical bar times open vertical bar straight b close vertical bar times cos space straight theta end cell equals 3 end table end style 

Maka nilai dari begin mathsize 14px style vertical line straight a with bar on top plus straight b with bar on top vertical line end style sebagai berikut 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight a plus straight b close vertical bar end cell equals cell square root of open vertical bar straight a close vertical bar squared plus open vertical bar straight b close vertical bar squared plus 2 times open vertical bar straight a close vertical bar times open vertical bar straight b close vertical bar times cosθ end root end cell row blank equals cell square root of open parentheses square root of 3 close parentheses squared plus open parentheses 1 close parentheses squared plus 3 end root end cell row blank equals cell square root of 3 plus 1 plus 3 end root end cell row blank equals cell square root of 7 end cell end table end style 

Jadi begin mathsize 14px style open vertical bar straight a with bar on top plus straight b with bar on top close vertical bar equals square root of 7 end style

93

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