Решите уравнения подробно

X (x-3) (4-x) = 16-x (x-3,5) ²

(4x-1) ² - (2x-3) (6x+5) = 4 (x-2) ²+16x

(x-1) (x+1) = 2 (x-5) ²-x (x-3)

№1

x[x*4-x*x-3*4-3 * (-x) ] = 16-x[x^2-2*x*3,5 + (3,5) ^2]

x (4x-x^2-12+3x) = 16-x (x^2-7x+12,25)

x (4x+3x-x^2-12) = 16-x (x^2-7x+12,25)

x (7x-x^2-12) = 16-x*x^2-x * (-7x) - x*12,25

x*7x-x*x^2-x*12 = 16-x^3+7x^2-12,25x

7x^2-x^3-12x-16+x^3-7x^2+12,25x = 0 (сокращаются 7x^2 и - 7x^2, - х^3 и x^3)

-12x+12,25x-16 = 0

0,25x-16 = 0

0,25x = 16

x = 16:0,25 = > 16:1/4 = 16*4

x = 64

№2

[ (4x) ^2-2*4x*1+1^2] - (2x*6x+2x*5-3*6x-3*5) = 4 (x^2-2*x*2+2^2) + 16x

16x^2-8x+1 - (12x^2+10x-18x-15) = 4 (x^2-4x+4) + 16x

16x^2-8x+1 - (12x^2-8x-15) = 4*x^2-4*4x+4*4+16x

16x^2-8x+1-12x^2+8x+15 = 4x^2-16x+16+16x (сокращаются - 8x и 8x, - 16x

и 16x)

16x^2+1-12x^2+15 = 4x^2+16

16x^2-12x^2+1+15 = 4x^2+16

4x^2+16 = 4x^2+16

4x^2-4x^2 = 16-16

0=0

№3

x*x+x*1-1*x-1*1 = 2 (x^2-2*x*5+5^2) - x*x-x * (-3)

x^2+x-x-1 = 2 (x^2-10x+25) - x^2+3x (сокращаются х и - х)

x^2-1 = 2*x^2-2*10x+2*25-x^2+3x

x^2-1 = 2x^2-20x+50-x^2+3x

x^2-1 = 2x^2-x^2-20x+3x+50

x^2-1 = x^2-17x+50

x^2-x^2+17x-1-50 = 0 (сокращаются x^2 и - x^2)

17x-51 = 0

17x = 51

x = 51:17

х = 3