(2х-5)^2(х-5) = (2х-5)(х-5)^2

(2х-5)^2(х-5) = (2х-5)(х-5)^2
(2х-5)^2(х-5) - (2х-5)(х-5)^2=0
(2x-5)(x-5)((2x-5)-(x-5))=0
(2x-5)(x-5)(2x-5-x+5)=0
(2x-5)(x-5)(x)=0
(x-2.5)(x-5)(x)=0
X1=2.5
X2=5
X3=0

(2х-5)^2(х-5) = (2х-5)(х-5)^2 -> (2х-5)^2(х-5) - (2х-5)(х-5)^2 = 0 -> (2х-5)(х-5)x = 0 ->

2х-5 = 0

х-5 = 0

x = 0

(2x-5) = a
(x-5) = b

a^2 * b = a * b^2
a^2 * b - a * b^2 = 0
a * b * (a - b) = 0
a = 0 ------------------------------------> 2x - 5 = 0 --------> x = 5/2
b = 0 ------------------------------------> x - 5 = 0 ---------> x = 5
a - b = 0 ---------> a = b -------------> 2x - 5 = x - 5 ----> x = 0

x=0, x=5/2, x=5

2х * (5х - 7) = 2х^2 - 5;

10х^2 - 14х = 2х^2 - 5;

10х^2 - 2х^2 - 14х + 5 = 0;

8х^2 - 14х + 5 = 0;

D = b^2 - 4ac = 196 - 4 * 8 * 5 = 196 - 160 = 36.

D > 0, уравнение имеет два корня.

x1 = (-b + √D)/2a = (14 + 6)/16 = 20/16 = 1 1/4;

x2 = (-b - √D)/2a = (14 - 6)/16 = 8/16 = 1/2.

Ответ: х1 = 1 1/4; х2 = 1/2.

2) (х - 5)^2 = 3х^2 - х + 14;

х^2 - 10х + 25 = 3х^2 - х + 14;

2х^2 + 9х - 11 = 0;

D = b^2 - 4ac = 81 + 4 * 2 * 11 = 169;

x1 = (-b + √D)/2a = (-9 + 13)/4 = 4/4 = 1;

x2 = (-b - √D)/2a = (-9 - 13)/4 = -22/4 = -5 2/4 = -5 1/2.

Ответ: х1 = 1; х2 = -5 1/2.