Question

if √x+1/(2√x)=✓3 then x^2+1/(16x^2)=???​

Answer 1

$\sqrt{x} + \frac{1}{2 \sqrt{x} } = 3 \\ {( \sqrt{x} + \frac{1}{2 \sqrt{x} })}^{2} = {3}^{2} \\ x + \frac{1}{4x} + 2. \sqrt{x} . \frac{1}{2 \sqrt{x} } = 9 \\ x + \frac{1}{4x} + 1 = 9 \\ x + \frac{1}{4x} = 8 \\ {(x + \frac{1}{4x} )}^{2} = {8}^{2} \\ {x}^{2} + \frac{1}{16 {x}^{2} } + 2.x. \frac{1}{4x} = 64 \\ {x}^{2} + \frac{1}{16 {x}^{2} } + \frac{1}{2} = 64 \\ {x}^{2} + \frac{1}{16 {x}^{2} } = 64 - 0.5 \\ {x}^{2} + \frac{1}{16 {x}^{2} } = 63.5$