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.