1) (x-2,5)² = 45
x² - 5x + 6,25 = 45
x² - 5x - 38,75 = 0
a=1, b=-5, c=-38,75
D = b² - 4ac = (-5)² - 4*1*(-38,75) = 25 + 155 = 180 > 0
x1 = -b + √D/2a = 5 + √180/2;
x2 = -b - √D/2a = 5 - √180/2;
Ответ : 5+√180/2; 5 -√180/2;
4) (5x+1)² = 400
25x² + 10x + 1 = 400
25x² + 10x - 399 = 0
a1=25, b=10, c=-399
k = b/2 = 10/2 = 5;
D1 = k² - ac= 5² - 25*(-399) = 25 + 9975 = 10000 = 100² > 0
D1 > 0
x1 = -k + √D1/a = -5 + 100/25 = 95/25 = 3,8;
x2 = -k + √D1/a = -5 - 100/25 = -105/25 = 4,2;
Ответ : 3,8; 4,2;
2) (3-2x)² = 0,04;
9 - 12x + 4x² = 0,04;
4x² - 12x + 9 - 0,04 = 0
4x² - 12x + 8,96 = 0
a=4, b=-12, c=8,96
k = b/2 = -12/2 = -6
D1 = k² - ac = (-6)² - 4*8,96 = 36 - 35,84 = 0,16 = (0,4)² > 0
D1 > 0
x1 = -k+√D1/a = 6+0,4/4 = 6,4/4 = 1,6;
x2 = -k-√D1/a = 6-0,4/4 = 5,6/4 = 1,4;
Ответ : 1,6; 1,4;