please solve

9(x²+1/x²)-9(x+1/x)-52 = 0

9(x² + 2 + 1/x² -2)-9(x+1/x)-52 = 0

9((x + 1/x)² -2) - 9(x + 1/x) - 52 = 0

9(x + 1/x)² - 9(x+1/x) - 70 = 0

9Y² - 9Y - 70 = 0

Y = -7/3 and 10/3.

x + 1/x = 10/3

3x² - 10x + 3 = 0  

x = 2/3 and 6.

Similarly we can obtain the x values for Y = -7/3.

Regards,

Team,

TopperLearning.