При каких 3начениях х верно равенство:
а) (5х + 3)2 = 5(х + 3);
б) (3х + 10)2 = 3(х + 10);
в) (3х - 8)2 = 3х2 - 8x;
г) (4х + 5)2 = 5x2 + 4х;
д) (5x + 3)2 = 5х + 3;
е) (5x + 3)2 = (3x + 5)2;
ж) (4x + 5)2 = 4(х + 5)2;
3) (2х + 10)2 = 4(x + 5)2?


Решение:


а) (5х + 3)2 = 5(х + 3); 25х2 + 30х + 9 = 5х + 15; 25х2 + 25х - 6 = 0;
D = 252 + 4 • 25 • 6 = 625 + 600 = 1225; x = (-25±35)/50; x1 = -60/50 = -1 1/5; x2 = 1/5;
б) (3х + 10)2 = 3(х + 10); 9х2 + 60х + 100 = 3х + 30; 9х2 + 57х + 70 = 0;
D = 572 - 4 • 9 • 70 = 3249 - 2520 = 729; х = (-57±27)/18; x1 = -84/18 = -14/3; х2 = -30/18 = -5/3 = -1 2/3;
в) (3х - 8)2 = 3х2 - 8x; 9х2 - 48х + 64 = 3х2 - 8х; 6х2 - 40х + 64 = 0; 3х2 - 20х + 32 = 0;
D1 = 102 -32 • 3 = 100 - 96 = 4; х = (10±2)/3; x1 = 4; x2 = 8/3 = 2 2/3;
г) (4х + 5)2 = 5х2 + 4х; 16х2 + 40х + 25 = 5х2 + 4х; 11х2 + 36х + 25 = 0;
D1 = 182 - 11 • 25 = 324 - 275 = 49; х = (-18±7)/11; x1 = -1; x2 = -25/11 = 2 3/11;
д) (5x + 3)2 = 5х + 3; (5x + 3)2 - (5х + 3) = 0; (5х + 3) (5х + 3 - 1) = 0; 5х + 3 = 0 или 5х + 2 = = 0;
х1 = -3/5; х2 = -2/5;
е) (5x + 3)2 = (3x + 5)2;
1) 5х + 3 = 3x + 5; 2х = 2; х = 1;
2) 5х + 3 = - (3х + 5); 8х = -8; х = -1 => х = ±1;
ж) (4x + 5)2 = 4(х + 5)2; 16х2 +40х + 25 = 4х2 + 40х + 100; 12х2 - 75 - 0; х2 = 75/12 = 25/4; х = ±5/2 = ±2 1/2;
з) (2х + 10)2 = 4(x + 5)2; 4х2 + 40х + 100 = 4х2 + 40х + 100; х - любое число.



Похожие задачи: