Question

if x2+1/25x2=43/5 find the value of x+1/5x​

Answer 1

${x}^{2} + \frac{1}{25 {x}^{2} } = \frac{43}{5}$

using a²+b²=(a+b)²-2ab

$( {x + \frac{1}{5x} })^{2} - 2.x. \frac{1}{5x} = \frac{43}{5} \\ \\ ( {x + \frac{1}{5x} })^{2} - 2 = \frac{43}{5} \\ \\ ( {x + \frac{1}{5x} })^{2} = \frac{43}{5} + 2 \\ \\ ( {x + \frac{1}{5x} })^{2} = \frac{53}{5} \\ \\ x + \frac{1}{5x} = \sqrt{ \frac{53}{5} }$