Question

please
$if \: \\ {x}^{2} + \frac{1}{ {25x}^{2} } = 8 \times \frac{3}{5} \\ {then \: find \: the \: value \: of } \\ x + \frac{1}{5x}$

Answer 1

expand (x+1÷5x)² = x²+1/25x²+2/5

given x²+1/25x² = 24/5

substituting, (x+1/5x)² = 24/5+2/5=26/5

∴(x+1/5x) = √26/√5

Answer 2

Answer:

$Consider \: {(x + \frac{1}{5x} )}^{2} = {x}^{2} + \frac{1}{ {25x}^{2} } + 2 \times x \times \frac{1}{5x} \\ = 8 \frac{3 }{5} + \frac{2}{5} \\ = \frac{43}{5} + \frac{2}{5} \\ = \frac{45}{5} \\ = 9 \\ therefore \: x + \frac{1}{5x} = \sqrt{9} = 3$