Question

3√x/5 + 3√ 5/x = 10
please help me to find its roots ...​

Answer 1

Step-by-step explanation:

As i understand ur question...

$3 \sqrt{ \frac{x}{5} } + 3 \sqrt{ \frac{5}{x} } = 10 \\ 3( \frac{ \sqrt{5} }{ \sqrt{x} } + \frac{ \sqrt{x} }{ \sqrt{5} } ) = 10 \\ 3( \frac{5 + x}{ \sqrt{5x} } ) = 10 \\ 15 + 3x = 10 \sqrt{5x} \\ 3x - 10 \sqrt{5x} + 15 = 0 \\ 3x - 9 \sqrt{5x} - \sqrt{5x} + 15 = 0 \\ 3 \sqrt{x} ( \sqrt{x} - 3 \sqrt{5} ) - \sqrt{5} ( \sqrt{x} - 3 \sqrt{5} )=0 \\ ( \sqrt{x} - 3 \sqrt{5} )(3 \sqrt{x} - \sqrt{5} ) = 0 \\ \\ \sqrt{x } - 3 \sqrt{5} = 0 \\ \sqrt{x} = 3 \sqrt{5} \\ x = (3 \sqrt{5} )^{2} = 45 \\ \\ 3 \sqrt{x} - \sqrt{5} = 0 \\ \sqrt{x} = \frac{ \sqrt{5} }{3} \\ x = \frac{5}{9}$

Required Ans....

Thank you

..