Question

Решите уравнение: 1) 8(x-2)^9=0 2) 2x^3 * x^5-2=0 3)5x^7=0 4) x^6=1 5)7x^7 * x-7=0 6) 14(x+1)^7=0

Answer 1

1) 8(x-2)⁹=0

(x-2)⁹=0

x=2

2) 2x³*x⁵-2=0

2x⁸-2=0

x⁸=1

x1= 1, x2= -1

3) 5x⁷=0

x=0

4) x⁶=1

x1= 1, x2= -1

5) 7x⁷*x-7=0

7x⁸-7=0

x⁸=1

x1= 1, x2= -1

6) 14(x+1)⁷=0

x= -1

Answer 2

▪1) 2

▪2) ±1

▪3) 0

▪4) ±1

▪5) ±1

▪6) -1

Объяснение:

▪1)

$8(x - 2) ^{9} = 0 \\ (x - 2) ^{9} = 0 \\ x - 2 = 0 \\ x = 2$

▪2)

$2 {x}^{3} \times {x}^{5} - 2 = 0 \\ 2 {x}^{8} = 2 \\ {x}^{8} = 1 \\ x = ±1$

▪3)

$5 {x}^{7} = 0 \\ {x}^{7} = 0 \\ x = 0$

▪4)

${x}^{6} = 1 \\ x = ±1 \:$

▪5)

$7 {x}^{7} \times x - 7 = 0 \\ 7 {x}^{8} = 7 \\ {x}^{8} = 1 \\ x = ±1 \:$

▪6)

$14( {x + 1)}^{7} = 0 \\ {(x + 1)}^{7} = 0 \\ x + 1 = 0 \\ x = - 1$