Question

if x²+1/x²= 6 find x⁴+1/x⁴​

Answer 1

$\large \star \: \: \sf \large \fbox \red{Given - }$

$\: \: \: \: \sf {x}^{2} + \frac{1}{ {x}^{2} } = 6$

$\large \star \: \: \sf \large \fbox \red{To \:find - }$

$\: \: \: \: \sf {x}^{4} + \frac{1}{ {x}^{4} } \: = \: ?$

$\large \star \: \: \sf \large \fbox \red{solution \: - }$

$\: \: \: \: \sf {x}^{2} + \frac{1}{ {x}^{2} } = 6$

$\sf \: [squaring \: on \: both \: side]$

$\longrightarrow \sf \: { ({x}^{2} + \frac{1}{ {x}^{2} } ) }^{2} = {6}^{2}$

$\longrightarrow \sf \: {( {x}^{2}) }^{2} + { (\frac{1}{ {x}^{2} } )}^{2} + {2x}^{2} \times \frac{1}{ {x}^{2} } = 36$

$\longrightarrow \sf \: {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 36$

$\longrightarrow \sf \: {x}^{4} + \frac{1}{ {x}^{4} } = 36 - 2$

$\longrightarrow \sf \fbox \green{ x⁴ + 1/x⁴ = 34}$

Hope it's helpful...

Answer 2

HOPE IT HELPS YOU...................