Question

Please solve the problem

Answer 1

Step-by-step explanation:

there is the answer check it is correct

Answer 2

$\huge \bold \color{green}{ \underline{ \underline \red{required \: answer}}}$

$\bold{{ \underline{ \underline \orange{answer}}}} \orange{→}$

${ \tt \frac{3 + \sqrt{5} }{2} } \: \: \: \: \: \: \tt{and } \: \: \: \: \: \: { \tt \frac{3 - \sqrt{5} }{2} }$

$\bold{{ \underline{ \underline \orange{solution}}}} \orange{→}$

$\blue{\bold{x + \frac{1}{x} = 3 \: \: \: \: } } \: \: \: \: \\ \\ \bold{ \implies \: \frac{ {x}^{2} + 1}{x} = 3 } \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies \: {x}^{2} + 1 = 3x } \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies \: {x}^{2} - 3x + 1 = 0 }$

it's a quadratic equation which is in the form of ax²+bx+c = 0

here, a = 1 , b = -3 and c = 1

solve by quadratic formula

$\pink{ \bold{x = \frac{ - b \: ± \: \sqrt { \: {b}^{2} - 4ac} }{2a} }}$

so

$\bold{x = \frac{ - ( - 3)±</p><p> \sqrt{ {(3)}^{2} - 4 \times 1 \times 1} }{2 \times 1} } \\ \\ \bold{ \implies \: x = \frac{3±</p><p> \sqrt{9 - 4} }{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies \: x = \frac{3±</p><p> \sqrt{5} }{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies \: x = \frac{3 + \sqrt{5} }{2} \: \: , \: x = \frac{3 - \sqrt{5} }{2} } \: \: \: \: \: \: \:$

hence, roots of equation is (3+√5)/2 and (3-√5)/2