Question

if
$x + \frac{1}{x} = 4 \: then \: x - \frac{1}{x} =$

!????????

Answer 1

$hey \\ \\ here \: is \: your \: answer \\ \\ (x + \frac{1}{x} ) {}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ \\ 16 - 2 = {x}^{2} + \frac{1}{ {x}^{2} } \\ {x}^{2} + \frac{1}{x {}^{2} } = 14 \\ \\ \\ (x - \frac{1}{ {x}^{2} } ) {}^{2} = 14 - 2 = 12 \\ \\ x - \frac{1}{x} = \sqrt{12}$


Hope it helps!

Answer 2

Heya !!!



( X + 1/X ) = 4



( X + 1/X )² = (4)² [ On squaring both sides ]



X² + 1/X² + 2 × X × 1/X = 16


X² + 1/X² = 16 - 2


X² + 1/X² = 14



Let X - 1/X = Z



( X - 1/X)² = ( Z )² [ On squaring both sides ]


X² + 1/X² - 2 × X × 1/X = Z²


X² + 1/X² - 2 = Z²



14 - 2 = Z²



Z² = 12



Z = + ✓12 or -✓12



X - 1/X = (+-) ✓12.



★ HOPE IT WILL HELP YOU ★