a) lg² x - lg x + 1 = 9/lg10x ;

lg² x - lg x + 1 = 9/lg10x

lg² x - lg x + 1 = 9/(lg10 + lgx)

lg² x - lg x + 1 = 9/(1 + lgx)

Пусть t = lg x, тогда:

t² - t + 1 = 9/(1 + t)

(t² - t + 1)(1 + t) = 9

t³ + t² - t² - t + t + 1 = 9

t³ = 8

t = 2

lg x = 2

x = 10²

x = 100

Ответ: 100