Question

if x²+1/x²=38 find x⁴+1/x⁴​

Answer 1

Answer:

1442

Step-by-step explanation:

x²+1/x² = 38

=> (x²)²+(1/x²)² = (38)²

=> x⁴+1/x⁴+2 = 1444

=> x⁴+1/x⁴ = 1444 - 2

=> x⁴+1/x⁴ = 1442

Answer 2

Answer:

${x}^{4} + \frac{1}{ {x}^{4} } = 1442$

Step-by-step explanation:

$\underline{Given :} \\ {x}^{2} + \frac{1}{ {x}^{2} } = 38 \\ \\ \underline{Solution :} \\ {( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = { ({x}^{2}) }^{2} + \frac{ {1}^{2} }{ ({ {x}^{2}) }^{2} } + (2 \times {x}^{2} \times \frac{1}{ {x}^{2} } ) \\ {(38)}^{2} = {(x)}^{2 \times 2} + \frac{1}{ {(x)}^{2 \times 2} } + (2 \times \cancel{ {x}^{2}} \times \frac{1}{ \cancel{ {x}^{2} }} ) \\ 1444 = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \\ 1444 - 2 = {x}^{4} + \frac{1}{ {x}^{4} } \\ \boxed{ \underline{ \underline{ \bf 1442}} = {x}^{4} + \frac{1}{ {x}^{4} } }$