Question

x^2(1/x-2)=7/2 solve it.

Answer 1

Please see the attachment

Answer 2

$\underline{\mathbb{\red{SOLUTION}}}$ ➡

$\bold{ x{}^{2} ( \frac{1}{x - 2} ) = \frac{7}{2} } \\ \\ \bold{ = > \frac{x {}^{2} }{x - 2} = \frac{7}{2} } \\ \\ \bold{ = > 2 x {}^{2} = 7x - 14 } \\ \\ \bold{ = > 2x {}^{2} - 7x + 14 = 0}$

$\bold{Now,} \\ \\ \boxed{\bold{x = \frac{ - b ± \sqrt[]{b {}^{2} - 4ac \: \: } }{2a} }}$



$\bold{Here,} \\ \bold{a = 2} \\ \bold{b = - 7} \\ \bold{c = 14} \\ \\ \bold{So,} \\ \\ \bold{x = \frac{ - b ± \sqrt{b {}^{2} - 4ac \: } }{2a} } \\ \\ = \bold{ \frac{ - ( - 7) ± \sqrt{( - 7) {}^{2} - 4 \times 2 \times 14 } }{2 \times 2} } \\ \\ \bold{ = \frac{7 ± \sqrt{49 - 112} }{4} } \\ \\ \bold{ = \frac{7 ± \sqrt{ - 63} }{4} } \\ \\ \bold{ = \frac{7 ± 3 \sqrt{ - 7} }{4} }\\ \\ \bold{ = \frac{7 ± 3 \sqrt{ 7}\:i }{4} \: \: \: \: \: \: \: \: [ As , \: \: \sqrt{-1} = i ]}$

$\bold{Hence,} \\ \\ \boxed{\bold{x = \frac{7 + 3 \sqrt{ 7} \: i }{4} \: \: \:, \: \: \: x = \frac{7 - 3 \sqrt{ 7} \: i}{4} }}$

________________________________________

✝$\mathfrak{\red{THANKS...}}$✝