Roboguru

Diketahui vektor , , dan . Tentukan nilai !

Diketahui vektor a with rightwards arrow on top equals left parenthesis 2 comma negative 3 right parenthesisb with rightwards arrow on top equals left parenthesis x comma negative 1 right parenthesis, dan open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar equals 5. Tentukan nilai x!

Jawaban:

Ingat rumus menentukan panjang vektor untuk vektor pada dua dimensi yaitu a with rightwards arrow on top equals square root of x squared plus y squared end root.

Menentukan a with rightwards arrow on top minus b with rightwards arrow on top terlebih dahulu.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top minus b with rightwards arrow on top end cell equals cell open parentheses 2 comma negative 3 close parentheses minus left parenthesis x comma negative 1 right parenthesis end cell row blank equals cell open parentheses 2 minus x comma negative 2 close parentheses end cell end table

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared end root end cell row 5 equals cell square root of left parenthesis 2 minus x right parenthesis squared plus left parenthesis negative 2 right parenthesis squared end root end cell row 5 equals cell square root of 4 minus 4 x plus x squared plus 4 end root end cell row 5 equals cell square root of x squared minus 4 x plus 4 plus 4 end root end cell row 5 equals cell square root of x squared minus 4 x plus 8 end root end cell row cell 5 squared end cell equals cell open parentheses square root of x squared minus 4 x plus 8 end root close parentheses squared end cell row 25 equals cell x squared minus 4 x plus 8 end cell row 0 equals cell x squared minus 4 x plus 8 minus 25 end cell row 0 equals cell x squared minus 4 x minus 17 end cell end table

Ubah menjadi bentuk kuadrat sempurna.

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 4 x minus 17 end cell equals 0 row cell x squared minus 4 x end cell equals 17 row cell left parenthesis x minus 2 right parenthesis squared minus 4 end cell equals 17 row cell left parenthesis x minus 2 right parenthesis squared end cell equals cell 17 plus 4 end cell row cell left parenthesis x minus 2 right parenthesis squared end cell equals 21 row cell x minus 2 end cell equals cell square root of 21 end cell row x equals cell 2 plus-or-minus square root of 21 end cell end table

Dari hasil diatas didapat x equals 2 plus square root of 21 atau x equals 2 minus square root of 21.

Jadi, dapat disimpulkan bahwa nilai x adalah 2 plus square root of 21 atau 2 minus square root of 21.

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