Решить уравнение. a). (1/5-2x)^2=(1/10-2x)^2. b). (x-1/4)^2=x^2. c). (x+1/4)^2=9x^2

a) (1/5 - 2x)^2 = (1/10 - 2x)^2;

1/25 - 1/5 * 2 * 2x + 4х^2 = 1/100 - 2 * 1/10 * 2x + 4x^2;

1/25 - 1/5 * 2 * 2x + 4х^2 - 4x^2 = 1/100 - 2 * 1/10 * 2x;

1/25 - 1/5 * 2 * 2x = 1/100 - 2 * 1/10 * 2x;

1/25 - 1/5 * 4x = 1/100 - 1/10 * 4x;

1/25 - 4/5x = 1/100 - 4/10x;

Домножим обе доли на 100:

1/25 * 100 - 4/5x * 100 = 1/100 * 100 - 4/10x * 100;

4 - 400/5х = 1 - 400/10х;

4 - 80х = 1 - 40х;

-80х + 40х = 1 - 4;

-40х = -3;

х = -3 : (-40);

х = 0,075.

b) (x - 1/4)^2 = x^2;

x^2 - 2 * 1/4 * х  + 1/16 = x^2;

-2 * 1/4 * х  + 1/16 = 0;

-2/4х = -1/16;

1/2х = 1/16;

х = 1/16 * 2/1;

х = 2/16;

х = 1/8.

c) (x + 1/4)^2 = 9x^2;

x^2 + 2 * 1/4 * x + 1/16 = 9x^2;

x^2 + 2/4x + 1/16 = 9x^2;

x^2 - 9x^2 + 2/4x = -1/16;

-8x^2  + 0,5x + 0.0625 = 0;

D = b^2 - 4ac = 0,25 + 4 * 8 * 0.0625 = 0,25 + 2 = 2,25.

D = 2,25 = 1,5.

x1 = (-b + D)/2a = (-0,5 + 1,5)/2 * (-8) = 1/-16 = -1/16.

x2 = (-b - D)/2a = (-0,5 - 1,5)/2 * (-8) = -2/-16 = 2/16 = 1/8.