Question

Solve for x:

2($x^2$+ 1/$x^2$) – 9(x + 1/x) + 14 = 0

Answer 1

$x^2$ + 1/$x^2$= (x + 1/x)${}^2$ – 2 [Using $(a+b{)}^2$ formula​]

2[(x + 1/x)${}^2$– 2 ] – 9(x + 1/x) + 14 = 0

Let x + 1/x = y

Therefore 2[$y^2$– 2] – 9y + 14 = 0

2$y^2$– 4 – 9y +14 = 0

2$y^2$– 9y +10 = 0

(y – 2)(2y – 5)= 0

y = 2 or y = 5/2

When x + 1/x = 2

$x^2$– 2x + 1 = 0

(x – 1)${}^2$= 0

x = 1

When x + 1/x = 5/2

$2x^2$– 5x + 2 = 0

x= 2 or x = 1/2

Therefore x = 1/2 , 1, 2