Question

solve the following equation and find all the possible values of x.



6(x^2 +1/x^2)-25(x-1/x)+ 12= 0​

Answer 1

Step-by-step explanation:

Given equation

6(x2 + 1/x2) – 25(x – 1/x) + 12 = 0

Put x – 1/x = y, squaring (x – 1/x)2 = y2

⇒ x2 + 1/x2 – 2 = y2

⇒ x2 + 1/x2 = y2 + 2

Now, given equation becomes

6(y2 + 2) – 25y + 12 = 0

⇒ 6y2 + 12 – 25y + 12 = 0

⇒ 6y2 – 25y + 24 = 0

⇒ 6y2 - 16y - 9y + 24 = 0

⇒ 2y(3y – 8) – 3(3y – 8) = 0

⇒ (3y – 8)(2y – 3) = 0

⇒ 3y – 8 = 0 or 2y – 3 = 0

⇒ 3y = 8 or 2y = 3

⇒ 3y = 8 or 2y = 3

⇒ y = 8/3 or y = 3/2

But x – 1/x = y