Solve for  x  :  2[x2 + 1x2] − 9[x + 1x] + 14  =  0  :Select an answerA 12, 1, 2 B 2, 4, 13 C 13, 4, 1 DNone of these

The given equation is 2[x² + 1/x²] - 9[x + 1/x] + 14 = 0

Let's substitute y = x + 1/x. Then y² = x² + 2 + 1/x², which simplifies the equation to:

2[y² - 2] - 9y + 14 = 0 2y² - 9y + 10 = 0 y² - 4.5y + 5 = 0

This is a quadratic equation in the form of ay² + by + c = 0. We can solve for y using the quadratic formula y = [-b ± sqrt(b² - 4ac)] / 2a:

y = [4.5 ± sqrt((4.5)² - 415)] / 2 y = [4.5 ± sqrt(20.25 - 20)] / 2 y = [4.5 ± sqrt(0.25)] / 2 y = [4.5 ± 0.5] / 2 y = 2.5 or y = 2

Substituting y = x + 1/x back in, we get:

x + 1/x = 2.5 x² - 2.5x + 1 = 0

and

x + 1/x = 2 x² - 2x + 1 = 0

Solving these quadratic equations, we get x = 1, 2, 1/2. So the answer is A : 1, 2, 1/2.