Question

x+1/x=3 so find the value of x⁴+1/x⁴=?​

Answer 1

Step-by-step explanation:

Hey buddy,

x + 1/x = 3

Squaring both sides,

(x + 1/x)² = 3^2

x² + 1/x² + 2×x×1/x = 9

x² + 1/x² + 2 = 9

x² + 1/x² = 7

Now, again squaring both sides,

(x² + 1/x²)² = 7²

x⁴ + 1/x⁴ + 2×x²×1/x²  = 49

x⁴ + 1/x⁴ + 2 = 49

∴ x⁴ + 1/x⁴ = 47

Answer 2

$\huge\mathfrak\red{Answer}$

$x + \frac{1}{x} = 3 \\ \\ squaring \: on \: both \: side \\ \\ {(x + \frac{ 1 }{x} )}^{2} = 9 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2(x)( \frac{1}{x} ) = 9 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ \\ take \: square \: on \: both \: sides \\ \\ {( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = 49 \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2( {x}^{2} )( \frac{1}{ {x}^{4} } ) = 49 \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 49 \\ \\ |answer | \\ {x}^{4} + \frac{1}{ {x}^{4} } = 47$