Question

If 2x - 1/x = 4 , then show that x^2+1/4x^2 =5​

Answer 1

Step-by-step explanation:

$HEY! \\\\ 2x-\frac{1}{x} =4 \\ \\=> multiply \ the \ numerator \ and \ denominator \ of \ (\frac{1}{x}) \ term \ by \ 2. \\\\ 2x-\frac{1}{x} (\frac{2}{2})=4 \\\\ 2x-\frac{2}{2x}=4 \\\\ 2(x-\frac{1}{2x})=4 \\\\ x-\frac{1}{2x}=\frac{4}{2} \\\\ => x-\frac{1}{2x}=2 \\\\\\ x^{2} +\frac{1}{4x^{2} } =? \\\\ x-\frac{1}{2x}=2 \ \ \ [squaring \ on \ both \ sides] \\\\ (x-\frac{1}{2x})^{2}=2^{2}$

$[(a-b)^{2} = a^{2} + b^{2}-2ab ] \\\\ x^{2} + (\frac{1}{2x})^{2}-2(x)(\frac{1}{2x})=4 \\\\x^{2} + \frac{1}{4x^{2} } - 1=4 \\\\ x^{2} + \frac{1}{4x^{2} }=4+1 \\\\=> x^{2} + \frac{1}{4x^{2} }=5 \\\\\\ HOPE \ IT \ HELPS..!$