Решите уравнение:
а) (х + 2)2 + (х - 3)2 = 13;
б) (3х - 5)2 - (2х + 1)2 = 24;
в) (х - 4)(x2 + 4х + 16) + 28 = x2(x - 25);
г) (2х + 1)(4x2 - 2х + 1) - 1 = 1,6x2(5х - 2).
Решение:
а) (х + 2)2 + (х - 3)2 = 13; x2 + 4х + 4 + x2 - 6x + 9 = 13; 2x2 - 2х = 0; 2х(х - 1) = 0 => x1 = 0; x2 = 1;
б) (3х - 5)2 - (2х + 1)2 = 24; 9x2 - 30x + 25 - (4x2 + 4х + 1) = 24; 9x2 - 30x + 25 - 4x2 - 4x - 1 = 24;
5x2 - 34x = 0; х(5х - 34) = 0 => х1 = 0; x2 = 34/5 = б,8;
в) (х - 4)(x2 + 4х + 16) + 28 = x2(x - 25); х3 + 4x2 + 16x - 4x2 - 16x - 64 + 28 = х3 - 25x2;
25x2 - 36 - 0; x2 = 36/25; х = ±6/5 = ±1,2;
г) (2х + 1)(4x22 - 2х + 1) - 1 = 1,6x2(5х - 2); 8x3 - 4x2 + 2х + 4x2 - 2x + 1 - 1 = 8х3 - 3,2x2; 3,2x2 = 0; x = 0.
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