• Помогите решить уравнение с модулями(срочно) |x+1|-|x|+3|x-1|-2|x-2|=|x+2|

Ответы 1

  • |x + 1| - |x| + 3 * |x - 1| - 2 * |x - 2| = |x + 2|;Модуль раскрывается со знаком плюс и минус. Получаем систему уравнений:{ |x + 1| - |x| + 3 * |x - 1| - 2 * |x - 2| = x + 2; |x + 1| - |x| + 3 * |x - 1| - 2 * |x - 2| = - x - 2;{ x + 1 - |x| + 3 * |x - 1| - 2 * |x - 2| = x + 2;- x - 1 - |x| + 3 * |x - 1| - 2 * |x - 2| = x + 2; x + 1 - |x| + 3 * |x - 1| - 2 * |x - 2| = - x - 2;- x - 1 - |x| + 3 * |x - 1| - 2 * |x - 2| = - x - 2; { - |x| + 3 * |x - 1| - 2 * |x - 2| = x + 2 - x - 1;- |x| + 3 * |x - 1| - 2 * |x - 2| = x + 2 + x + 1;- |x| + 3 * |x - 1| - 2 * |x - 2| = - x - 2 - x - 1;- |x| + 3 * |x - 1| - 2 * |x - 2| = - x - 2 + x + 1;{ - |x| + 3 * |x - 1| - 2 * |x - 2| = 1;- |x| + 3 * |x - 1| - 2 * |x - 2| = 2 * x + 3;- |x| + 3 * |x - 1| - 2 * |x - 2| = - 2 * x - 3;- |x| + 3 * |x - 1| - 2 * |x - 2| = - 1;{ - x + 3 * |x - 1| - 2 * |x - 2| = 1;x + 3 * |x - 1| - 2 * |x - 2| = 1;- x + 3 * |x - 1| - 2 * |x - 2| = 2 * x + 3;x + 3 * |x - 1| - 2 * |x - 2| = 2 * x + 3;- x + 3 * |x - 1| - 2 * |x - 2| = - 2 * x - 3;x + 3 * |x - 1| - 2 * |x - 2| = - 2 * x - 3;- x + 3 * |x - 1| - 2 * |x - 2| = - 1;x + 3 * |x - 1| - 2 * |x - 2| = - 1;{ 3 * |x - 1| - 2 * |x - 2| = 1 + x;3 * |x - 1| - 2 * |x - 2| = 1 - x;3 * |x - 1| - 2 * |x - 2| = 3 * x + 3;3 * |x - 1| - 2 * |x - 2| = x + 3;3 * |x - 1| - 2 * |x - 2| = - x - 3;3 * |x - 1| - 2 * |x - 2| = - 3 * x - 3;3 * |x - 1| - 2 * |x - 2| = - 1 + x;3 * |x - 1| - 2 * |x - 2| = - 1 - x;{ 3 * (x - 1) - 2 * |x - 2| = 1 + x;- 3 * (x - 1) - 2 * |x - 2| = 1 + x;3 * (x - 1) - 2 * |x - 2| = 1 - x;- 3 * (x - 1) - 2 * |x - 2| = 1 - x;3 * (x - 1) - 2 * |x - 2| = 3 * x + 3;- 3 * (x - 1) - 2 * |x - 2| = 3 * x + 3;3 * (x - 1) - 2 * |x - 2| = x + 3;- 3 * (x - 1) - 2 * |x - 2| = x + 3;3 * (x - 1) - 2 * |x - 2| = - x - 3;- 3 * (x - 1) - 2 * |x - 2| = - x - 3;3 * (x - 1) - 2 * |x - 2| = - 3 * x - 3;- 3 * (x - 1) - 2 * |x - 2| = - 3 * x - 3;3 * (x - 1) - 2 * |x - 2| = - 1 + x;- 3 * (x - 1) - 2 * |x - 2| = - 1 + x;3 * (x - 1) - 2 * |x - 2| = - 1 - x;- 3 * (x - 1) - 2 * |x - 2| = - 1 - x;{ - 2 * |x - 2| = 4 - 2 * x;- 2 * |x - 2| = - 2 + 4 * x;- 2 * |x - 2| = 4 - 4 * x;- 2 * |x - 2| = - 2 + 2 * x;- 2 * |x - 2| = 6;- 2 * |x - 2| = 6 * x;- 2 * |x - 2| = - 2 * x + 6;- 2 * |x - 2| = 4 * x;- 2 * |x - 2| = - 4 * x;- 2 * |x - 2| = - 2 * x - 6;- 2 * |x - 2| = - 6 * x;- 2 * |x - 2| = - 6;- 2 * |x - 2| = 2 - 2 * x;- 2 * |x - 2| = - 4 + 4 * x;- 2 * |x - 2| = 2 - 4 * x;- 2 * |x - 2| = - 4 + 2 * x;{ 2 * |x - 2| = 2 * x - 4;2 * |x - 2| = 2 - 4 * x; 2 * |x - 2| = 4 * x - 4;2 * |x - 2| = 2 - 2 * x;2 * |x - 2| = - 6;2 * |x - 2| = - 6 * x;2 * |x - 2| = 2 * x - 6;2 * |x - 2| = 4 * x;2 * |x - 2| = 4 * x;2 * |x - 2| = 2 * x + 6; 2 * |x - 2| = 6 * x; 2 * |x - 2| = 6; 2 * |x - 2| = 2 * x - 2; 2 * |x - 2| = 4 - 4 * x;2 * |x - 2| = 4 * x - 2;2 * |x - 2| = 2 * x - 4;{ - 2 * x + 4 = 2 * x - 4;2 * x - 4 = 2 - 4 * x;- 2 * x + 4 = 2 - 4 * x; 2 * x - 4 = 4 * x - 4; - 2 * x + 4 = 4 * x - 4;2 * x - 4 = 2 - 2 * x;2 * x - 4 = - 6;- 2 * x + 4 = - 6;2 * x - 4 = - 6 * x;- 2 * x + 4 = - 6 * x;- 2 * x + 4 = 2 * x - 6;2 * x - 4 = 4 * x;- 2 * x + 4 = 4 * x;2 * x - 4 = 4 * x;- 2 * x + 4 = 4 * x;- 2 * x + 4 = 2 * x + 6; 2 * x - 4 = 6 * x;- 2 * x + 4 = 6 * x; 2 * x - 4 = 6;- 2 * x + 4 = 6; - 2 * x + 4 = 2 * x - 2; 2 * x - 4 = 4 - 4 * x; - 2 * x + 4 = 4 - 4 * x;2 * x - 4 = 4 * x - 2;- 2 * x + 4 = 4 * x - 2;- 2 * x + 4 = 2 * x - 4;{ x = 2;x = 1;x = - 1; x = 0;x = 4/3;x = 3/2;x = 5;x = 1/2;x = 5/2;x = - 2;x = 2/3;x = - 1/2; x = - 3/2;x = 4.
    • Автор:

      mini me
    • 5 лет назад
    • 0
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