Question

x^2+1/2x^2=23 than find the value of x-1/x​

Answer 1

$\frac{ {x}^{2} + 1 }{ {2x}^{2} } = 23 \\ \\ {x}^{2} + 1 = {46x}^{2} \\ \\ {46x}^{2} - {x}^{2} = 1 \\ \\ {45x}^{2} = 1 \\ x = \sqrt{ \frac{1}{45} } \\ \\ x = \frac{1}{3 \sqrt{5} } \\ x = \frac{3 \sqrt{5} }{45} \\ x = \frac{ \sqrt{5} }{15} \\ \\ \frac{1}{x} = \frac{1}{ \frac{ \sqrt{5} }{15} } \\ \\ \frac{1}{x} = \frac{15}{ \sqrt{5} } \\ \frac{1}{x } = \frac{15 \sqrt{5} }{5} \\ \frac{1}{x} = \frac{3 \sqrt{5} }{5} \\ x - \frac{1}{x} = \frac{ \sqrt{5} - 9 \sqrt{5} }{15} = \frac{ - 8 \sqrt{5} }{15}$

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