Разложите на множители: а) 16х^4-81y^4 б)48a^4-3b^4 в)1/81m^8-1 г)32-1\2 m^6

а) 16х^4-81y^4=(4x^2-9y^2)(4x^2+9y^2)=(2x-3y)(2x+3y)(4x^2+9y^2)

б)48a^4-3b^4=3(4a^2-b^2)(4a^2+b^2)=3(2a-b)(2a++b^2)

в)1/81m^8-1=(1/9m^4-1)(1/9m^4+1)=(1/3m^2-1)(1/3m^2+/9m^4+1=(1/v3 m-1)(1/v3 m+1)(1/3m^2+/9m^4+1)

г)32-1\2 m^6=1/2(64-m^6)=1/2(8-m^3)(8+m^3)=1/2(2-m)(4+2m+m^2)(2+m)(4-2m+m^2)

1)   27*2^x-8*3^x=0   /3^x 27*(2/3)^x - 8 = 0 (2/3)^x = 8/27 (2/3)^x = (2/3)^3 x = 3 ответ: х = 3 2)   2^(x+1) - 2^(x-1)=3^(2-x) 2*(2^x) - (1/2)*(2^x)   =  9/(3^x) (2^x) *(2 - 1/2)  =  9/(3^x) (2^x)*(3/2)  =  9/(3/2)     (6^x) = 6^1 x = 1 ответ: х = 1 3)   9*(4^x)  -  13*(6^x) +  4*(9^x)  =  0   9*(2^2x)    -  13*(2^x)*(3^x) +  4*(3^2x)  =  0   /(3^2x) 9*(2/3)^2x - 13*(2/3)^x + 4 = 0 (2/3)^x = t 9t^2 - 13t + 4 = 0 d = 169 - 4*9*4 = 25 t1 = (13 - 5)/18 t1 = 4/9 t2 = (13 + 5)/18  t2 = 1 1)   (2/3)^x = 4/9 (2/3)^x = (2/3)^2 x1 = 2 2)   (2/3)^x = 1 (2/3)^x = (2/3)^0 x2 = 0 ответ: x1 = 2; x2 = 1

6* (- 5 - 7х) = - 8х + 2 30 + 42х = - 8х + 2 42х + 8х = 2 - 30 50х = - 28 х = - 28 : 50 х = - 0,56 проверка: - 6 * (- 5 - 7 * (- 0,56) = - 8 * (- 0,56) + 2                   - 6 * (- 1,08) = 4,48 + 2                   6,48 = 6,48 9 + 2 * (2х + 1) = 1 9 + 4х + 2 = 1 4х = 1 - 9 - 2 4х = - 10 х = - 10 : 4 х = - 2,5 проверка: 9 + 2 * (2 * (- 2,5) + 1) = 1                   9 + 2 * (- 4) = 1                   9 + (- 8) = 1                   1 = 1