Pertanyaan

Banyaknya bilangan bulat lebih kecil dari 8 yang memenuhi pertidaksamaan x + 5 1 + x − 7 1 + x − 5 1 + x + 7 1 ≥ 0 adalah....

Banyaknya bilangan bulat lebih kecil dari 8 yang memenuhi pertidaksamaan $\frac{1}{x + 5} + \frac{1}{x - 7} + \frac{1}{x - 5} + \frac{1}{x + 7} \geq 0$ adalah....

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Pembahasan

Bilangan bulat yang lebih kecil daripada 8 adalah { -4, -3, -2, -1, 0, 6) ada 6 bilangan.

$fraction numerator 1 over denominator x plus 5 end fraction plus fraction numerator 1 over denominator x minus 7 end fraction plus fraction numerator 1 over denominator x minus 5 end fraction plus fraction numerator 1 over denominator x plus 7 end fraction greater or equal than 0 fraction numerator x minus 5 plus x plus 5 over denominator left parenthesis x plus 5 right parenthesis left parenthesis x minus 5 right parenthesis end fraction plus fraction numerator x plus 7 plus x minus 7 over denominator left parenthesis x plus 7 right parenthesis left parenthesis x minus 7 right parenthesis end fraction greater or equal than 0 fraction numerator 2 x over denominator x squared minus 25 end fraction plus fraction numerator 2 x over denominator x squared minus 49 end fraction greater or equal than 0 2 x open parentheses fraction numerator 1 over denominator x squared minus 25 end fraction plus fraction numerator 1 over denominator x squared minus 49 end fraction close parentheses greater or equal than 0 2 x open parentheses fraction numerator x squared minus 49 plus x squared minus 25 over denominator open parentheses x squared minus 25 close parentheses open parentheses x squared minus 49 close parentheses end fraction close parentheses greater or equal than 0 2 x open parentheses fraction numerator 2 x squared minus 74 over denominator open parentheses x squared minus 25 close parentheses open parentheses x squared minus 49 close parentheses end fraction close parentheses greater or equal than 0 2 x open parentheses fraction numerator 2 left parenthesis x squared minus 37 right parenthesis over denominator open parentheses x squared minus 25 close parentheses open parentheses x squared minus 49 close parentheses end fraction close parentheses greater or equal than 0 4 x fraction numerator open parentheses x plus 37 close parentheses left parenthesis x minus 37 right parenthesis over denominator left parenthesis x plus 5 right parenthesis left parenthesis x minus 5 right parenthesis left parenthesis x plus 7 right parenthesis left parenthesis x minus 7 right parenthesis end fraction greater or equal than 0$