Question

If m+1/m=3, then prove , m= (3+√5)/2

Answer 1

${ \bold{ \boxed{ \boxed{ \mathtt{ \huge \red{answer}}}}}}$

${ \bold{ \underline{Given }: - }}$

${ \bold{ \orange{m + \frac{1}{m} = 3 }}}$

${ \bold{ \underline\red{ To \: \: prove}} : - } \\ \\ { \bold{ \orange{m = \frac{3 + \sqrt{5} }{2} }}} \\ \\ \\ \\ { \bold{ \boxed{ \boxed{\red{ \huge{ \bigstar \: solution \bigstar}}}}}} \\ \\ \\ { \bold{ \orange{ \implies \: m + \frac{1}{m} = 3 }}} \\ \\ \\ { \bold{ \orange{ \implies \: {m}^{2} + 1 = 3m }}} \\ \\ \\ { \bold{ \orange{ \implies \: {m}^{2} - 3m + 1 = 0 }}} \\ \\ \\ { \bold{ \orange{ \implies \:m = \frac{3 + \sqrt{9 - 4(1)} }{2} \: \: and \: \: m = \frac{3 - \sqrt{9 - 4} }{2} }}} \\ \\ { \bold{ \orange{ \implies \: m = \frac{3 + \sqrt{5} }{2} \: \: and \: \: m = \frac{3 - \sqrt{5} }{2} }}} \\ \\ { \bold{ \orange{ \implies \:{ \boxed{ m = \frac{3 + \sqrt{5} }{2} }}}}} \: \: { \bold{ \orange{ \: and}}} \: \: { \bold{ \orange{ \boxed{m = \frac{3 - \sqrt{5} }{2} }}}} \\ \\ \\ { \bold{ \green{ \implies \: used \: \: formula \: : - }}} \\ \\ { \bold{ \blue{ \: \: \: \: \: . \: \: if \: \: a {x}^{2} + bx + c = 0 \: \: is \: \: an \: \: quadratic \: \: equation}}} \\ { \bold{ \blue{ \: \: \: \: \: \: \: \: then \: \: roots \: \: are \: \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \: \: and \: \: x = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} }}}$