Question

x+1/x=5/2 quadratic equations

Answer 1

Here is your solution

$x + \frac{1}{x} = \frac{5}{2} \\ \\ \frac{x { }^{2} + 1 }{x} = \frac{5}{2} \\Cross\: multiplication \\ 2(x {}^{2} + 1) = 5 \times x \\ \\ 2x {}^{2} + 2 = 5x \\ \\ 2x {}^{2} - 5x + 2=0$

Answer 2

$your \: given \: equation \: is \: \\ \\ \: \: \: \: \: \: x \: + \: \frac{1}{x} \: = \: \frac{5}{2} \\ \\ now \: taking \: lcm \: on \: lhs\: \\ \\ \: \: \: \: \: \: \frac{ {x}^{2} + \: 1 }{x} \: = \: \frac{5}{2} \\ \\ \: \: \: \: \: \: \frac{ {x}^{2} \: + \: 1 }{x} \: - \: \frac{5}{2} = \: 0 \\ \\ taking \: \: lcm \\ \\ \: \: \: \frac{ ({x}^{2} \: + \: 1) \times 2 \: - \: (5 \times x) }{(2 \times x)} = \: 0 \\ \\ \: \: \: \: \frac{ 2{x}^{2} + \: 2 \: - \: 5x }{2x} \: = \: 0 \\ \\ \: \: \: \: 2{x}^{2} \: - \: 5x \: + 2 \: = \: 0 \\ \\ \: \: \: here \: is \: your \: required \: answer \:$