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Persamaan kuadrat x2−6x+m=0 mempunyai akar-akar x1​ dan x2​. Jika x1​−x2​=12 maka nilai dari x12​+x22​ sama dengan...

Pertanyaan

Persamaan kuadrat x squared minus 6 x plus m equals 0 mempunyai akar-akar x subscript 1 dan x subscript 2. Jika x subscript 1 minus x subscript 2 equals 12 maka nilai dari x subscript 1 squared plus x subscript 2 squared sama dengan...

  1. 90

  2. 80

  3. 72

  4. 40

  5. 18

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 6 x plus m end cell equals 0 row cell a x squared plus b x plus c end cell equals 0 row a equals 1 row b equals cell negative 6 end cell row c equals m end table

Karena x subscript 1 minus x subscript 2 equals 12 maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 minus x subscript 2 end cell equals cell fraction numerator square root of D over denominator a end fraction end cell row 12 equals cell fraction numerator square root of b squared minus 4 a c end root over denominator a end fraction end cell row 12 equals cell fraction numerator square root of open parentheses negative 6 close parentheses squared minus 4 open parentheses 1 close parentheses open parentheses m close parentheses end root over denominator 1 end fraction end cell row 12 equals cell square root of 36 minus 4 m end root end cell row 144 equals cell 36 minus 4 m end cell row cell 4 m end cell equals cell 36 minus 144 end cell row cell 4 m end cell equals cell negative 108 end cell row m equals cell negative 108 divided by 4 end cell row m equals cell negative 27 end cell end table

Di dapatkan nilai m equals negative 27.

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 6 x plus m end cell equals 0 row cell x squared minus 6 x minus 27 end cell equals 0 row cell left parenthesis x minus 9 right parenthesis left parenthesis x plus 3 right parenthesis end cell equals 0 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 9 end cell equals 0 row cell x subscript 1 end cell equals 9 row blank blank atau row cell x plus 3 end cell equals 0 row cell x subscript 2 end cell equals cell negative 3 end cell end table

Di dapatkan x subscript 1 equals 9 dan x subscript 2 equals negative 3

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 squared plus x subscript 2 squared end cell equals cell 9 squared plus open parentheses negative 3 close parentheses squared end cell row blank equals cell 81 plus 9 end cell row blank equals 90 end table


Jadi,  nilai dari x subscript 1 squared plus x subscript 2 squared sama dengan 90.

 

Oleh karena itu, jawaban yang benar adalah A.

53

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