Pl. answer this question

a(x²+1) -  x(a²+1) = 0 

ax² -  (a² + 1)x + a   = 0

x = {(a² + 1) ± [(a² + 1)²-4a²]}/2a

= {(a² + 1) ± [(a⁴ + 2a²+ 1 - 4a²]}/2a

= {(a² + 1) ±[(a⁴ - 2a²+ 1]}/2a

= {(a² + 1) ±[(a² - 1]}/2a

= a and 1/a

Writing  the quadratic  equation, in standard roots form, i.e. x²- (α+β)x + αβ = 0 

x²- (a + 1/a)x + 1 = 0

ax² - (a²+1)x + a = 0

which is exactly identical to the given quadratic equation.

Regards,

Team,

TopperLearning.