Question

Which of the following are quadratic equation in x? 

`(x + 1/x)^2 = 2(x + 1/x) + 3`

Answer 1

`(x + 1/x)^2 = -2(x + 1/x) + 3` 

⇒ `((x^2 + 1)/x)^2 = 2((x^2 + 1)/x) + 3` 

⇒ (x² + 1)² = 2x(x² + 1) + 3x² 

⇒ x⁴ + 2x² + 1 = 2x³ + 2x + 3x² 

⇒ x⁴ – 2x³ – x² – 2x + 1 = 0 

This is not of the form ax² – bx + c = 0 

Hence, the given equation is not a quadratic equation.