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TequilaSunrise
@TequilaSunrise
July 2022
1
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ребят, помогите, пожалуйста, очень нужно, прошу!
один из примеров решить 2 способами. Всего 3 примера должно выйти (из 2)
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karasikov
2.
2(x^2 + x + 1)^2 - 7(x - 1)^2 = 13(x^3 - 1);
a = x - 1;
b = x^2 + x + 1;
2b^2 - 7a^2 = 13ab;
2b^2 - 13ab - 7a^2 = 0;
(b - 7a)(2b + a) = 0;
1)b = 7a; 2)2b = -a;
1) x^2 + x + 1 = 7x - 7;
x^2 - 6x + 8 = 0;
(x - 4)(x - 2) = 0;
x = 4, x = 2;
2) 2x^2 + 2x + 2 + x - 1 = 0;
2x^2 + 3x + 1 = 0;
(2x + 1)(x + 1) = 0;
x = -0.5, x = -1;
Ответ: x = -1, -0.5, 2, 4.
3.
x^2/(1 - 2x^2) = 12x^2 +7x - 6;
x^2/(1 - 2x^2) + 1 = 12x^2 + 7x - 6 + 1;
(x^2 + 1 - 2x^2)/(1 - 2x^2) = 12x^2 + 7x - 5;
(1 + x)(1 - x)/(1 - 2x^2) = (12x - 5)(x + 1);
(x + 1) * ( (1 - x)/(1 - 2x^2) - 12x + 5) = 0;
(x + 1) * ( (1 - x)/(1 - 2x^2) - 12x + 6 - 1)) = 0;
(x + 1) * ( (1 - x - 1 + 2x^2)/(1 - 2x^2) - 12x + 6)
) = 0;
(x + 1) * ( (2x^2 - x)/(1 - 2x^2) - 6(2x - 1))
) = 0;
(x + 1) * (2x - 1) * (x/(1 - 2x^2) - 6) = 0;
(x + 1) * (2x - 1) * (x - 6 + 12x^2)/
(1 - 2x^2
) = 0;
(x + 1) * (2x - 1) * (x - 2/3) * (x + 3/4) /
(1 - 2x^2
) = 0;
ответ: x = -1, x = 1/2, x = 2/3, x = -3/4.
2 votes
Thanks 1
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Answers & Comments
2(x^2 + x + 1)^2 - 7(x - 1)^2 = 13(x^3 - 1);
a = x - 1;
b = x^2 + x + 1;
2b^2 - 7a^2 = 13ab;
2b^2 - 13ab - 7a^2 = 0;
(b - 7a)(2b + a) = 0;
1)b = 7a; 2)2b = -a;
1) x^2 + x + 1 = 7x - 7;
x^2 - 6x + 8 = 0;
(x - 4)(x - 2) = 0;
x = 4, x = 2;
2) 2x^2 + 2x + 2 + x - 1 = 0;
2x^2 + 3x + 1 = 0;
(2x + 1)(x + 1) = 0;
x = -0.5, x = -1;
Ответ: x = -1, -0.5, 2, 4.
3.
x^2/(1 - 2x^2) = 12x^2 +7x - 6;
x^2/(1 - 2x^2) + 1 = 12x^2 + 7x - 6 + 1;
(x^2 + 1 - 2x^2)/(1 - 2x^2) = 12x^2 + 7x - 5;
(1 + x)(1 - x)/(1 - 2x^2) = (12x - 5)(x + 1);
(x + 1) * ( (1 - x)/(1 - 2x^2) - 12x + 5) = 0;
(x + 1) * ( (1 - x)/(1 - 2x^2) - 12x + 6 - 1)) = 0;
(x + 1) * ( (1 - x - 1 + 2x^2)/(1 - 2x^2) - 12x + 6)) = 0;
(x + 1) * ( (2x^2 - x)/(1 - 2x^2) - 6(2x - 1))) = 0;
(x + 1) * (2x - 1) * (x/(1 - 2x^2) - 6) = 0;
(x + 1) * (2x - 1) * (x - 6 + 12x^2)/(1 - 2x^2) = 0;
(x + 1) * (2x - 1) * (x - 2/3) * (x + 3/4) / (1 - 2x^2) = 0;
ответ: x = -1, x = 1/2, x = 2/3, x = -3/4.