Question

решите уравнение х в 8=(4х-5) в 4

Answer 1

${x}^{8} = {(4x - 5)}^{4} \\ {( {x}^{2} )}^{4} = {(4x - 5)}^{4}$
$1) \: \: {x}^{2} = 4x - 5 \\ {x}^{2} - 4x + 5 = 0$
D = 16 - 4 • 5 = 16 - 20 = - 4 , D < 0
Корней нет

$2) \: \: {x}^{2} = - (4x - 5) \\ {x}^{2} = - 4x + 5 \\ {x}^{2} + 4x - 5 = 0$
D = 16 + 4 • 5 = 16 + 20 = 36

x1 = ( - 4 - 6 ) / 2 = - 10 / 2 = - 5

x2 = ( - 4 + 6 ) / 2 = 2 / 2 = 1


ОТВЕТ: - 5 ; 1