Question

a(x^2+1)=x(a^2+1) , find the roots of the following equation ​

Answer 1

Answer:

=> x = a, 1/a

Step-by-step explanation:

Given, quadratic equation is

=> a(x2 + 1) - x(a2 + 1) = 0

=> ax2 + a - xa2 - x = 0

=> ax2 - (a2 + 1)x + a = 0

Using quadratic formula, we get

=> x = [-{-(a2 + 1)} ± √{(a2 + 1)2 - 4 * a * a}]/2a

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

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

=> x = [(a2 + 1) ± √{(a2 - 1)2 }]/2a

=> x = [(a2 + 1) ± (a2 - 1)]/2a

=> x = [(a2 + 1) + (a2 - 1)]/2a and x = [(a2 + 1) - (a2 - 1)]/2a

=> x = 2a2 /2a and x = 2/2a  

=> x = a, 1/a

So, the roots are a and 1/a